To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Question

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Answer 1

Question

Chapter 20, Problem 20.41E

(a)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(a)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=1038=0.2632p^2=x2n2=2034=0.5882

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.79p=0.0052

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(b)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(b)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=2230=0.7333p^2=x2n2=1838=0.4737

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.16p=0.0308

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(c)

To determine

To write a short description of your findings contrasting your results for part (a) and (b).

(c)

Expert Solution

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. From, part (a) we have the result as there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. And from part (b) we have the result as, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, for the women is forties, the proportion with increased LH levels is significantly greater in the placebo group and for the women is fifties and sixties, the proportion with increased LH levels is significantly greater in the melatonin group. Therefore, the effect is reversed in the two age groups.

(d)

To determine

To show that these results are not statistically significant.

(d)

Expert Solution

Answer to Problem 20.41E

We can conclude that there is no significant difference.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=3268=0.4706p^2=x2n2=3872=0.5278

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=0.68p=0.4988

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P>0.05⇒Fial to Reject H0

Thus, we can conclude that there is no significant difference since the pooling of the two groups cancels out the two separate effects.

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Answer 2

Question

Chapter 20, Problem 20.41E

(a)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(a)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=1038=0.2632p^2=x2n2=2034=0.5882

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.79p=0.0052

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(b)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(b)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=2230=0.7333p^2=x2n2=1838=0.4737

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.16p=0.0308

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(c)

To determine

To write a short description of your findings contrasting your results for part (a) and (b).

(c)

Expert Solution

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. From, part (a) we have the result as there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. And from part (b) we have the result as, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, for the women is forties, the proportion with increased LH levels is significantly greater in the placebo group and for the women is fifties and sixties, the proportion with increased LH levels is significantly greater in the melatonin group. Therefore, the effect is reversed in the two age groups.

(d)

To determine

To show that these results are not statistically significant.

(d)

Expert Solution

Answer to Problem 20.41E

We can conclude that there is no significant difference.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=3268=0.4706p^2=x2n2=3872=0.5278

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=0.68p=0.4988

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P>0.05⇒Fial to Reject H0

Thus, we can conclude that there is no significant difference since the pooling of the two groups cancels out the two separate effects.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 20, Problem 20.41E

(a)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(a)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=1038=0.2632p^2=x2n2=2034=0.5882

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.79p=0.0052

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(b)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(b)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=2230=0.7333p^2=x2n2=1838=0.4737

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.16p=0.0308

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(c)

To determine

To write a short description of your findings contrasting your results for part (a) and (b).

(c)

Expert Solution

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. From, part (a) we have the result as there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. And from part (b) we have the result as, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, for the women is forties, the proportion with increased LH levels is significantly greater in the placebo group and for the women is fifties and sixties, the proportion with increased LH levels is significantly greater in the melatonin group. Therefore, the effect is reversed in the two age groups.

(d)

To determine

To show that these results are not statistically significant.

(d)

Expert Solution

Answer to Problem 20.41E

We can conclude that there is no significant difference.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=3268=0.4706p^2=x2n2=3872=0.5278

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=0.68p=0.4988

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P>0.05⇒Fial to Reject H0

Thus, we can conclude that there is no significant difference since the pooling of the two groups cancels out the two separate effects.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 20, Problem 20.41E

(a)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(a)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=1038=0.2632p^2=x2n2=2034=0.5882

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.79p=0.0052

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(b)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(b)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=2230=0.7333p^2=x2n2=1838=0.4737

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.16p=0.0308

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(c)

To determine

To write a short description of your findings contrasting your results for part (a) and (b).

(c)

Expert Solution

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. From, part (a) we have the result as there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. And from part (b) we have the result as, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, for the women is forties, the proportion with increased LH levels is significantly greater in the placebo group and for the women is fifties and sixties, the proportion with increased LH levels is significantly greater in the melatonin group. Therefore, the effect is reversed in the two age groups.

(d)

To determine

To show that these results are not statistically significant.

(d)

Expert Solution

Answer to Problem 20.41E

We can conclude that there is no significant difference.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=3268=0.4706p^2=x2n2=3872=0.5278

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=0.68p=0.4988

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P>0.05⇒Fial to Reject H0

Thus, we can conclude that there is no significant difference since the pooling of the two groups cancels out the two separate effects.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 20, Problem 20.41E

(a)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(a)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=1038=0.2632p^2=x2n2=2034=0.5882

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.79p=0.0052

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(b)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(b)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=2230=0.7333p^2=x2n2=1838=0.4737

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.16p=0.0308

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(c)

To determine

To write a short description of your findings contrasting your results for part (a) and (b).

(c)

Expert Solution

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. From, part (a) we have the result as there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. And from part (b) we have the result as, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, for the women is forties, the proportion with increased LH levels is significantly greater in the placebo group and for the women is fifties and sixties, the proportion with increased LH levels is significantly greater in the melatonin group. Therefore, the effect is reversed in the two age groups.

(d)

To determine

To show that these results are not statistically significant.

(d)

Expert Solution

Answer to Problem 20.41E

We can conclude that there is no significant difference.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=3268=0.4706p^2=x2n2=3872=0.5278

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=0.68p=0.4988

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P>0.05⇒Fial to Reject H0

Thus, we can conclude that there is no significant difference since the pooling of the two groups cancels out the two separate effects.

Answer 6

Chapter 20, Problem 20.41E

(a)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

(a)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=1038=0.2632p^2=x2n2=2034=0.5882

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.79p=0.0052

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Answer 7

Chapter 20, Problem 20.41E

(a)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Answer 8

(a)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=1038=0.2632p^2=x2n2=2034=0.5882

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.79p=0.0052

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Answer 13

(b)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

(b)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=2230=0.7333p^2=x2n2=1838=0.4737

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.16p=0.0308

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Answer 14

(b)

To determine

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Answer 15

(b)

Expert Solution

Answer to Problem 20.41E

Yes, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Now, we want to know is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=2230=0.7333p^2=x2n2=1838=0.4737

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=2.16p=0.0308

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P<0.05⇒Reject H0

Thus, we have sufficient evidence to conclude that there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Answer 20

(c)

To determine

To write a short description of your findings contrasting your results for part (a) and (b).

(c)

Expert Solution

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. From, part (a) we have the result as there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. And from part (b) we have the result as, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, for the women is forties, the proportion with increased LH levels is significantly greater in the placebo group and for the women is fifties and sixties, the proportion with increased LH levels is significantly greater in the melatonin group. Therefore, the effect is reversed in the two age groups.

Answer 21

(c)

To determine

To write a short description of your findings contrasting your results for part (a) and (b).

Answer 22

(c)

Expert Solution

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. From, part (a) we have the result as there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties. And from part (b) we have the result as, there is significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties. Thus, for the women is forties, the proportion with increased LH levels is significantly greater in the placebo group and for the women is fifties and sixties, the proportion with increased LH levels is significantly greater in the melatonin group. Therefore, the effect is reversed in the two age groups.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

(d)

To determine

To show that these results are not statistically significant.

(d)

Expert Solution

Answer to Problem 20.41E

We can conclude that there is no significant difference.

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=3268=0.4706p^2=x2n2=3872=0.5278

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=0.68p=0.4988

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P>0.05⇒Fial to Reject H0

Thus, we can conclude that there is no significant difference since the pooling of the two groups cancels out the two separate effects.

Answer 27

(d)

To determine

To show that these results are not statistically significant.

Answer 28

(d)

Expert Solution

Answer to Problem 20.41E

We can conclude that there is no significant difference.

Answer 29

(d)

Expert Solution

Answer 30

(d)

Expert Solution

Answer 31

Expert Solution

Answer 32

Explanation of Solution

In the question, it is given that melatonin is a naturally occurring hormone involved in the regulation of body’s internal clock and is available as a dietary supplement in the United States. There is a table given for the treatment of melatonin and a placebo for women in forties and women in their fifties and sixties. Thus, we define the hypotheses as:

H0:p1=p2Ha:p1≠p2

That is, there is no statistical difference versus there is statistical difference.

The proportions are as:

p^1=x1n1=3268=0.4706p^2=x2n2=3872=0.5278

Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator TI−89 . Then select 6:2− PropZTest from the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded.

Thus, by using the calculator TI−89 , the test statistics and the P-value is as:

z=0.68p=0.4988

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

P>0.05⇒Fial to Reject H0

Thus, we can conclude that there is no significant difference since the pooling of the two groups cancels out the two separate effects.

Answer 33

Ch. 20 - Prob. 20.1AYK Ch. 20 - Prob. 20.2AYK Ch. 20 - Prob. 20.3AYK Ch. 20 - Prob. 20.4AYK Ch. 20 - Prob. 20.5AYK Ch. 20 - Prob. 20.6AYK Ch. 20 - Prob. 20.7AYK Ch. 20 - Prob. 20.8AYK Ch. 20 - Prob. 20.9AYK Ch. 20 - Prob. 20.10AYK

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their forties.

Answer to Problem 20.41E

Explanation of Solution

To explain is there significant evidence of a difference in the proportions of women with increased LH levels between women taking melatonin and women taking placebo, for women in their fifties and sixties.

Answer to Problem 20.41E

Explanation of Solution

To write a short description of your findings contrasting your results for part (a) and (b).

Explanation of Solution

To show that these results are not statistically significant.

Answer to Problem 20.41E

Explanation of Solution

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