A random sample of 14 college women and a random sample of 1

A random sample of 14 college women and a random sample of 19 college men were separately asked to estimate how much they spent on clothing in the last month. The accompanying table shows the data. Suppose the null hypothesis that the mean amount spent by men and the mean amount spent by women for clothing are the same could not be rejected using two-tailed test at a significance level of 0.05. Complete parts a through c below Click the icon to view the data table a. If a 95% confidence interval for the difference between means is found would it capture 0? Explain OA The 95% interval would not capture 0 because there appears to be a difference between the mean amounts spent on clo m trom looking at the data OB The 95% interval would not capture 0, because the hypothesis that the mean amounts spent on clothing are the same could not be rejected by the hypothesis test. OC The 95% interval would capture 0, because there does not appear to be a difference between the mean amounts spent on cloth ng rom looking at the data OD The 95% interval would capture 0 because the hypothesis that the mean amounts spent on clot m are he same could not ere cted ry: ne po e stiest b. If a 99% confidence interval for the difference between means is found, would it capture 0? Explain. A OB OC. OD. Yes. because a 99% nterval s wider han a 9590 mterval a d centered at he same value and based on the resu s o the pot es s test a 9 ter a would not capture No, because a 99% interval is narrower than a 95% nterval and centered at the same value, and based on the results of the hypothesis test, a 959 mterval would not capture 0 No, because a 99% mterval is narrower an a 95% interval and centered at the same va a and based on he resu s u e r o e s te a erval vould capture Yes, because a 99% nterval is wider than a 95% nterval and centered at the same va e and base onthe resu s o the h pot e stes a s omterva would carre

Solution

a) answer is c. since there is no difference in the means, the confidence interval will contian 0.

b) answer is D.

c) the 95% confidence interval is (-33,52)

because the interval does capture 0, the hypothesis that the mean difference in spending on clothing is 0 cannot be rejected which shows the hypothesis that the means are the same cannot be rejected and there is no significnat difference.