State the conclusion of the test.

Question

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Answer 1

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter B, Problem 1E

a.

To determine

State the conclusion of the test.

a.

Expert Solution

Answer to Problem 1E

The conclusion of the test is Reject H0.

Explanation of Solution

Here, denote μ1 as the mean recovery time of students with colds who are given large doses of vitamin C and μ2 as the mean recovery time of students with colds who are not given vitamin C.

The test hypotheses are given below:

Null hypothesis: H0:μ1=μ2

That is, the mean recovery time is the same for the students with colds who are given large doses of vitamin C and not given vitamin C.

Alternative hypothesis: Ha:μ1>μ2

That is, the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Rejection rule:

If the p-value≤significance level, reject the null hypothesis.

If the p-value>significance level, do not reject the null hypothesis.

Conclusion:

Here, the p-value of 0.003 is less than the 0.05 significance level.

From the rejection rule, the null hypothesis is rejected.

Hence, the conclusion is that there is evidence to conclude that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C at 5% of significance level.

b.

To determine

Delineate an inappropriate method of collecting the data that would bias the results so much that a conclusion based on the p-value is very unreliable.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Give vitamin C for the students who have had cold symptoms for a long time.
The latter may have shorter recovery times since the cold is almost over when they start treatment, while the students those who are not getting vitamin C might be at the early stages of their colds.

c.

To determine

Delineate an appropriate method of collecting the data that would permit to interpret the p-value to extend the results to a broader student population.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Randomize the students into two groups (using lot system or flip a coin)
Flip a coin to specify who gets vitamin C (heads) and who gets the placebo (tails).
Neither the participants nor the person determining when they recovered from cold must know the group they belong to.

d.

To determine

Make a conclusion about vitamin C as a treatment for the students with common cold using the p-value from the assumed data in Part (c).

d.

Expert Solution

Explanation of Solution

If the data are collected in the same way explained in Part (c), then it is assumed that the p-value obtained is small.

The small p-value indicates that the null hypothesis H0:μ1=μ2 is in favor of the alternative Ha:μ1<μ2. Therefore, there is strong evidence that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

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Answer 2

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter B, Problem 1E

a.

To determine

State the conclusion of the test.

a.

Expert Solution

Answer to Problem 1E

The conclusion of the test is Reject H0.

Explanation of Solution

Here, denote μ1 as the mean recovery time of students with colds who are given large doses of vitamin C and μ2 as the mean recovery time of students with colds who are not given vitamin C.

The test hypotheses are given below:

Null hypothesis: H0:μ1=μ2

That is, the mean recovery time is the same for the students with colds who are given large doses of vitamin C and not given vitamin C.

Alternative hypothesis: Ha:μ1>μ2

That is, the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Rejection rule:

If the p-value≤significance level, reject the null hypothesis.

If the p-value>significance level, do not reject the null hypothesis.

Conclusion:

Here, the p-value of 0.003 is less than the 0.05 significance level.

From the rejection rule, the null hypothesis is rejected.

Hence, the conclusion is that there is evidence to conclude that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C at 5% of significance level.

b.

To determine

Delineate an inappropriate method of collecting the data that would bias the results so much that a conclusion based on the p-value is very unreliable.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Give vitamin C for the students who have had cold symptoms for a long time.
The latter may have shorter recovery times since the cold is almost over when they start treatment, while the students those who are not getting vitamin C might be at the early stages of their colds.

c.

To determine

Delineate an appropriate method of collecting the data that would permit to interpret the p-value to extend the results to a broader student population.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Randomize the students into two groups (using lot system or flip a coin)
Flip a coin to specify who gets vitamin C (heads) and who gets the placebo (tails).
Neither the participants nor the person determining when they recovered from cold must know the group they belong to.

d.

To determine

Make a conclusion about vitamin C as a treatment for the students with common cold using the p-value from the assumed data in Part (c).

d.

Expert Solution

Explanation of Solution

If the data are collected in the same way explained in Part (c), then it is assumed that the p-value obtained is small.

The small p-value indicates that the null hypothesis H0:μ1=μ2 is in favor of the alternative Ha:μ1<μ2. Therefore, there is strong evidence that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

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Answer 3

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter B, Problem 1E

a.

To determine

State the conclusion of the test.

a.

Expert Solution

Answer to Problem 1E

The conclusion of the test is Reject H0.

Explanation of Solution

Here, denote μ1 as the mean recovery time of students with colds who are given large doses of vitamin C and μ2 as the mean recovery time of students with colds who are not given vitamin C.

The test hypotheses are given below:

Null hypothesis: H0:μ1=μ2

That is, the mean recovery time is the same for the students with colds who are given large doses of vitamin C and not given vitamin C.

Alternative hypothesis: Ha:μ1>μ2

That is, the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Rejection rule:

If the p-value≤significance level, reject the null hypothesis.

If the p-value>significance level, do not reject the null hypothesis.

Conclusion:

Here, the p-value of 0.003 is less than the 0.05 significance level.

From the rejection rule, the null hypothesis is rejected.

Hence, the conclusion is that there is evidence to conclude that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C at 5% of significance level.

b.

To determine

Delineate an inappropriate method of collecting the data that would bias the results so much that a conclusion based on the p-value is very unreliable.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Give vitamin C for the students who have had cold symptoms for a long time.
The latter may have shorter recovery times since the cold is almost over when they start treatment, while the students those who are not getting vitamin C might be at the early stages of their colds.

c.

To determine

Delineate an appropriate method of collecting the data that would permit to interpret the p-value to extend the results to a broader student population.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Randomize the students into two groups (using lot system or flip a coin)
Flip a coin to specify who gets vitamin C (heads) and who gets the placebo (tails).
Neither the participants nor the person determining when they recovered from cold must know the group they belong to.

d.

To determine

Make a conclusion about vitamin C as a treatment for the students with common cold using the p-value from the assumed data in Part (c).

d.

Expert Solution

Explanation of Solution

If the data are collected in the same way explained in Part (c), then it is assumed that the p-value obtained is small.

The small p-value indicates that the null hypothesis H0:μ1=μ2 is in favor of the alternative Ha:μ1<μ2. Therefore, there is strong evidence that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

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Answer 4

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter B, Problem 1E

a.

To determine

State the conclusion of the test.

a.

Expert Solution

Answer to Problem 1E

The conclusion of the test is Reject H0.

Explanation of Solution

Here, denote μ1 as the mean recovery time of students with colds who are given large doses of vitamin C and μ2 as the mean recovery time of students with colds who are not given vitamin C.

The test hypotheses are given below:

Null hypothesis: H0:μ1=μ2

That is, the mean recovery time is the same for the students with colds who are given large doses of vitamin C and not given vitamin C.

Alternative hypothesis: Ha:μ1>μ2

That is, the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Rejection rule:

If the p-value≤significance level, reject the null hypothesis.

If the p-value>significance level, do not reject the null hypothesis.

Conclusion:

Here, the p-value of 0.003 is less than the 0.05 significance level.

From the rejection rule, the null hypothesis is rejected.

Hence, the conclusion is that there is evidence to conclude that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C at 5% of significance level.

b.

To determine

Delineate an inappropriate method of collecting the data that would bias the results so much that a conclusion based on the p-value is very unreliable.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Give vitamin C for the students who have had cold symptoms for a long time.
The latter may have shorter recovery times since the cold is almost over when they start treatment, while the students those who are not getting vitamin C might be at the early stages of their colds.

c.

To determine

Delineate an appropriate method of collecting the data that would permit to interpret the p-value to extend the results to a broader student population.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Randomize the students into two groups (using lot system or flip a coin)
Flip a coin to specify who gets vitamin C (heads) and who gets the placebo (tails).
Neither the participants nor the person determining when they recovered from cold must know the group they belong to.

d.

To determine

Make a conclusion about vitamin C as a treatment for the students with common cold using the p-value from the assumed data in Part (c).

d.

Expert Solution

Explanation of Solution

If the data are collected in the same way explained in Part (c), then it is assumed that the p-value obtained is small.

The small p-value indicates that the null hypothesis H0:μ1=μ2 is in favor of the alternative Ha:μ1<μ2. Therefore, there is strong evidence that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

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

Answer 5

Chapter B, Problem 1E

a.

To determine

State the conclusion of the test.

a.

Expert Solution

Answer to Problem 1E

The conclusion of the test is Reject H0.

Explanation of Solution

Here, denote μ1 as the mean recovery time of students with colds who are given large doses of vitamin C and μ2 as the mean recovery time of students with colds who are not given vitamin C.

The test hypotheses are given below:

Null hypothesis: H0:μ1=μ2

That is, the mean recovery time is the same for the students with colds who are given large doses of vitamin C and not given vitamin C.

Alternative hypothesis: Ha:μ1>μ2

That is, the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Rejection rule:

If the p-value≤significance level, reject the null hypothesis.

If the p-value>significance level, do not reject the null hypothesis.

Conclusion:

Here, the p-value of 0.003 is less than the 0.05 significance level.

From the rejection rule, the null hypothesis is rejected.

Hence, the conclusion is that there is evidence to conclude that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C at 5% of significance level.

b.

To determine

Delineate an inappropriate method of collecting the data that would bias the results so much that a conclusion based on the p-value is very unreliable.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Give vitamin C for the students who have had cold symptoms for a long time.
The latter may have shorter recovery times since the cold is almost over when they start treatment, while the students those who are not getting vitamin C might be at the early stages of their colds.

c.

To determine

Delineate an appropriate method of collecting the data that would permit to interpret the p-value to extend the results to a broader student population.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Randomize the students into two groups (using lot system or flip a coin)
Flip a coin to specify who gets vitamin C (heads) and who gets the placebo (tails).
Neither the participants nor the person determining when they recovered from cold must know the group they belong to.

d.

To determine

Make a conclusion about vitamin C as a treatment for the students with common cold using the p-value from the assumed data in Part (c).

d.

Expert Solution

Explanation of Solution

If the data are collected in the same way explained in Part (c), then it is assumed that the p-value obtained is small.

The small p-value indicates that the null hypothesis H0:μ1=μ2 is in favor of the alternative Ha:μ1<μ2. Therefore, there is strong evidence that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Answer 6

Chapter B, Problem 1E

a.

To determine

State the conclusion of the test.

a.

Expert Solution

Answer to Problem 1E

The conclusion of the test is Reject H0.

Explanation of Solution

Here, denote μ1 as the mean recovery time of students with colds who are given large doses of vitamin C and μ2 as the mean recovery time of students with colds who are not given vitamin C.

The test hypotheses are given below:

Null hypothesis: H0:μ1=μ2

That is, the mean recovery time is the same for the students with colds who are given large doses of vitamin C and not given vitamin C.

Alternative hypothesis: Ha:μ1>μ2

That is, the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Rejection rule:

If the p-value≤significance level, reject the null hypothesis.

If the p-value>significance level, do not reject the null hypothesis.

Conclusion:

Here, the p-value of 0.003 is less than the 0.05 significance level.

From the rejection rule, the null hypothesis is rejected.

Hence, the conclusion is that there is evidence to conclude that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C at 5% of significance level.

Answer 7

Chapter B, Problem 1E

a.

To determine

State the conclusion of the test.

Answer 8

a.

Expert Solution

Answer to Problem 1E

The conclusion of the test is Reject H0.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Here, denote μ1 as the mean recovery time of students with colds who are given large doses of vitamin C and μ2 as the mean recovery time of students with colds who are not given vitamin C.

The test hypotheses are given below:

Null hypothesis: H0:μ1=μ2

That is, the mean recovery time is the same for the students with colds who are given large doses of vitamin C and not given vitamin C.

Alternative hypothesis: Ha:μ1>μ2

That is, the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Rejection rule:

If the p-value≤significance level, reject the null hypothesis.

If the p-value>significance level, do not reject the null hypothesis.

Conclusion:

Here, the p-value of 0.003 is less than the 0.05 significance level.

From the rejection rule, the null hypothesis is rejected.

Hence, the conclusion is that there is evidence to conclude that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C at 5% of significance level.

Answer 13

b.

To determine

Delineate an inappropriate method of collecting the data that would bias the results so much that a conclusion based on the p-value is very unreliable.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Give vitamin C for the students who have had cold symptoms for a long time.
The latter may have shorter recovery times since the cold is almost over when they start treatment, while the students those who are not getting vitamin C might be at the early stages of their colds.

Answer 14

b.

To determine

Delineate an inappropriate method of collecting the data that would bias the results so much that a conclusion based on the p-value is very unreliable.

Answer 15

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Give vitamin C for the students who have had cold symptoms for a long time.
The latter may have shorter recovery times since the cold is almost over when they start treatment, while the students those who are not getting vitamin C might be at the early stages of their colds.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

c.

To determine

Delineate an appropriate method of collecting the data that would permit to interpret the p-value to extend the results to a broader student population.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Randomize the students into two groups (using lot system or flip a coin)
Flip a coin to specify who gets vitamin C (heads) and who gets the placebo (tails).
Neither the participants nor the person determining when they recovered from cold must know the group they belong to.

Answer 20

c.

To determine

Delineate an appropriate method of collecting the data that would permit to interpret the p-value to extend the results to a broader student population.

Answer 21

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Randomize the students into two groups (using lot system or flip a coin)
Flip a coin to specify who gets vitamin C (heads) and who gets the placebo (tails).
Neither the participants nor the person determining when they recovered from cold must know the group they belong to.

Answer 22

c.

Expert Solution

Answer 23

c.

Expert Solution

Answer 24

Expert Solution

Answer 25

d.

To determine

Make a conclusion about vitamin C as a treatment for the students with common cold using the p-value from the assumed data in Part (c).

d.

Expert Solution

Explanation of Solution

If the data are collected in the same way explained in Part (c), then it is assumed that the p-value obtained is small.

The small p-value indicates that the null hypothesis H0:μ1=μ2 is in favor of the alternative Ha:μ1<μ2. Therefore, there is strong evidence that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.

Answer 26

d.

To determine

Make a conclusion about vitamin C as a treatment for the students with common cold using the p-value from the assumed data in Part (c).

Answer 27

d.

Expert Solution

Explanation of Solution

If the data are collected in the same way explained in Part (c), then it is assumed that the p-value obtained is small.

The small p-value indicates that the null hypothesis H0:μ1=μ2 is in favor of the alternative Ha:μ1<μ2. Therefore, there is strong evidence that the mean recovery time of students with colds who are given large doses of vitamin C is faster than those who are not given vitamin C.