Question

n order to compare the means of two populations, independent random samples of 475 observations are selected from each population, with the following results: Sample 1 Sample 2 ?⎯⎯⎯1=5228 ?⎯⎯⎯2=5165 ?1=120 ?2=160 (a) Use a 97 % confidence interval to estimate the difference between the population means (?1−?2). ≤(?1−?2)≤ (b) Test the null hypothesis: ?0:(?1−?2)=0 versus the alternative hypothesis: ??:(?1−?2)≠0. Using ?=0.03, give the following: (i) the test statistic ?= 1.963 (ii) the positive critical ? score (iii) the negative critical ? score The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=0. B. We can reject the null hypothesis that (?1−?2)=0 and accept that (?1−?2)≠0. (c) Test the null hypothesis: ?0:(?1−?2)=25 versus the alternative hypothesis: ??:(?1−?2)≠25. Using ?=0.03, give the following: (i) the test statistic ?= (ii) the positive critical ? score (iii) the negative critical ? score The final conclusion is A. We can reject the null hypothesis that (?1−?2)=25 and accept that (?1−?2)≠25. B. There is not sufficient evidence to reject the null hypothesis that (?1−?2)=25.

Please show all work, including finding the t values.

Answer 1