Question

Chapter 11 Homework 0 Saved Help Save & Exit Submit Check my work 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. 4.16 points Statistic Sample mean Sample standard deviation Sample size Men 24.07 5.70 Women 21.55 eBook Punt 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? References Motomen. (Negative values should a. State the decision rule for 001 significance level: Ho: Mononen Miten be indicated by a minus sign. Round your answers to 3 decimal places.) Reject Hift ort < Prev 4 of 12 !!! Next >

Answer 1

Given population standard deviations are equal for both the samples.

a) degrees of freeom df = n1+n2-2 = 36+39 -2 = 73

critical value = t0.005,73 = 2.645

Reject H0 if t < -2.645 or t> 2.645

b)

Descriptive Statistics

Sample	N	Mean	StDev
Men	36	24.07	5.70
Women	39	21.55	4.64

let suffix 1 be men and suffix 2 be women.

pooled std dev Sp = $\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}$ = 5.18

test statistic t = $\frac{\bar{x_{1}}-\bar{x_{2}}}{S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}}$ = 2.107

c) since test statistic is less than critical value We Fail to reject H0.

d) p-value = 0.039