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In: Statistics and Probability

A recent study focused on the number of times men and women who live alone buy...

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 but unknown. The information is summarized below,

Sample Mean

Sample Standard Deviation

Sample Size

Men

25

6

20

Women

23

4

22

At the 0.05 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? Please answer questions a to d. Please show all steps of derivation.

a. Write down the null hypothesis and the alternative hypothesis. (You can verbally describe if you do not know how to type in equations)  

b. State the decision rule for 0.05 significance level.

c. Compute the value of the test statistic.

d. What is your decision regarding the null hypothesis? What is your conclusion?

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