One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for wives and husbands. Conduct a hypothesis test at the 5% level to see if wife's satisfaction levels are lower than their husband's satisfaction level (meaning that, within the partnership, the husband is happier than the wife). Wife's score 3 2 3 3 4 2 1 1 2 4 Husband's score 2 2 1 3 2 1 1 1 2 4NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. H0: ?d = 0 H0: ?d > 0 H0: ?d < 0 H0: ?d ≠ 0 Part (b) State the alternative hypothesis. Ha: ?d > 0 Ha: ?d < 0 Ha: ?d = 0 Ha: ?d ≠ 0 Part (c) In words, state what your random variable Xd represents. Xd represents the average difference in the husbands' and the wives' satisfaction levels. Xd represents the difference in the satisfaction levels of husbands and wives. Xd represents the average satisfaction level of husbands and wives. Xd represents the difference in the average satisfaction level of husbands and wives. Part (d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.) Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) = Part (f) What is the p-value? p-value < 0.0100.010 < p-value < 0.050 0.050 < p-value < 0.100p-value > 0.100 Explain what the p-value means for this problem. If H0 is false, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is at most −0.6.If H0 is false, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is greater than −0.6. If H0 is true, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is greater than −0.6.If H0 is true, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is at most −0.6. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? = (ii) Decision: reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision: Since p-value > ?, we do not reject the null hypothesis.Since p-value < ?, we do not reject the null hypothesis. Since p-value < ?, we reject the null hypothesis.Since p-value > ?, we reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to support the claim that, on average, the husbands are more pleased than the wives with the division of childcare.There is not sufficient evidence to support the claim that, on average, the husbands are more pleased than the wives with the division of childcare. Part (i) Explain how you determined which distribution to use. The standard normal distribution will be used because the samples are independent and the population standard deviation is known.The t-distribution will be used because the samples are dependent. The standard normal distribution will be used because the samples involve the difference in proportions.The t-distribution will be used because the samples are independent and the population standard deviation is not known.

One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for wives and husbands. Conduct a hypothesis test at the 5% level to see if wife's satisfaction levels are lower than their husband's satisfaction level (meaning that, within the partnership, the husband is happier than the wife). Wife's score 3 2 3 3 4 2 1 1 2 4 Husband's score 2 2 1 3 2 1 1 1 2 4NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. H0: ?d = 0 H0: ?d > 0 H0: ?d < 0 H0: ?d ≠ 0 Part (b) State the alternative hypothesis. Ha: ?d > 0 Ha: ?d < 0 Ha: ?d = 0 Ha: ?d ≠ 0 Part (c) In words, state what your random variable Xd represents. Xd represents the average difference in the husbands' and the wives' satisfaction levels. Xd represents the difference in the satisfaction levels of husbands and wives. Xd represents the average satisfaction level of husbands and wives. Xd represents the difference in the average satisfaction level of husbands and wives. Part (d) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.) Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) = Part (f) What is the p-value? p-value < 0.0100.010 < p-value < 0.050 0.050 < p-value < 0.100p-value > 0.100 Explain what the p-value means for this problem. If H0 is false, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is at most −0.6.If H0 is false, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is greater than −0.6. If H0 is true, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is greater than −0.6.If H0 is true, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is at most −0.6. Part (g) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value. Part (h) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) ? = (ii) Decision: reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision: Since p-value > ?, we do not reject the null hypothesis.Since p-value < ?, we do not reject the null hypothesis. Since p-value < ?, we reject the null hypothesis.Since p-value > ?, we reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to support the claim that, on average, the husbands are more pleased than the wives with the division of childcare.There is not sufficient evidence to support the claim that, on average, the husbands are more pleased than the wives with the division of childcare. Part (i) Explain how you determined which distribution to use. The standard normal distribution will be used because the samples are independent and the population standard deviation is known.The t-distribution will be used because the samples are dependent. The standard normal distribution will be used because the samples involve the difference in proportions.The t-distribution will be used because the samples are independent and the population standard deviation is not known.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

Wife's score	3	2	3	3	4	2	1	1	2	4
Husband's score	2	2	1	3	2	1	1	1	2	4

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Part (a)

State the null hypothesis.

H₀: ?_d = 0

H₀: ?_d > 0

H₀: ?_d < 0

H₀: ?_d ≠ 0
Part (b)

State the alternative hypothesis.

H_a: ?_d > 0

H_a: ?_d < 0

H_a: ?_d = 0

H_a: ?_d ≠ 0
Part (c)

In words, state what your random variable
X_d
represents.

X_d
represents the average difference in the husbands' and the wives' satisfaction levels.
X_d
represents the difference in the satisfaction levels of husbands and wives.
X_d
represents the average satisfaction level of husbands and wives.
X_d
represents the difference in the average satisfaction level of husbands and wives.
Part (d)

State the distribution to use for the test. (Enter your answer in the form z or t_df where df is the degrees of freedom.)
Part (e)

What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)
=
Part (f)

What is the p-value?

p-value < 0.0100.010 < p-value < 0.050 0.050 < p-value < 0.100p-value > 0.100

Explain what the p-value means for this problem.
If
H₀
is false, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is at most −0.6.If
H₀
is false, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is greater than −0.6. If
H₀
is true, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is greater than −0.6.If
H₀
is true, then there is a chance equal to the p-value that the sample average difference between the husbands' scores and the wives' scores is at most −0.6.
Part (g)

Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.
Part (h)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:

reject the null hypothesisdo not reject the null hypothesis

(iii) Reason for decision:

Since p-value > ?, we do not reject the null hypothesis.Since p-value < ?, we do not reject the null hypothesis.    Since p-value < ?, we reject the null hypothesis.Since p-value > ?, we reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to support the claim that, on average, the husbands are more pleased than the wives with the division of childcare.There is not sufficient evidence to support the claim that, on average, the husbands are more pleased than the wives with the division of childcare.
Part (i)

Explain how you determined which distribution to use.
The standard normal distribution will be used because the samples are independent and the population standard deviation is known.The t-distribution will be used because the samples are dependent. The standard normal distribution will be used because the samples involve the difference in proportions.The t-distribution will be used because the samples are independent and the population standard deviation is not known.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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