Question

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.

Statistic	Men	Women
Sample mean	25.24	21.73
Sample standard deviation	5.53	4.54
Sample size	34	37

At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

1. State the decision rule for 0.01 significance level: H₀: μ_Men= μ_Women   H₁: μ_Men ≠ μ_Women. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

3. What is your decision regarding the null hypothesis?

4. What is the p-value? (Round your answer to 3 decimal places.)

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.

Statistic	Men	Women
Sample mean	25.24	21.73
Sample standard deviation	5.53	4.54
Sample size	34	37

At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

1. State the decision rule for 0.01 significance level: H₀: μ_Men= μ_Women   H₁: μ_Men ≠ μ_Women. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

3. What is your decision regarding the null hypothesis?

4. What is the p-value? (Round your answer to 3 decimal places.)

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.

Statistic	Men	Women
Sample mean	25.24	21.73
Sample standard deviation	5.53	4.54
Sample size	34	37

At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

1. State the decision rule for 0.01 significance level: H₀: μ_Men= μ_Women   H₁: μ_Men ≠ μ_Women. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

3. What is your decision regarding the null hypothesis?

4. What is the p-value? (Round your answer to 3 decimal places.)

Answer 1

1. State the decision rule for 0.01 significance level: H₀: μ_Men= μ_Women   H₁: μ_Men ≠ μ_Women. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

2.649

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

2.933

3. What is your decision regarding the null hypothesis?

Reject the null hypothesis.

4. What is the p-value? (Round your answer to 3 decimal places.)

​​​​​​​0.005

The output is:

Men	Women
25.24	21.73	mean
5.53	4.54	std. dev.
34	37	n
	69	df
	3.51000	difference (Men - Women)
	25.37953	pooled variance
	5.03781	pooled std. dev.
	1.19682	standard error of difference
	2.649	critical t
	2.933	t
	0.005	p-value (two-tailed)