Question

In order to compare the means of two populations, independent random samples of 385 observations are selected from each population, with the results found in the table to the right. Complete parts a through e.

Sample 1                                                 Sample 2

X1 = 5,337 X2 = 5,298

s1 = 157 s2 = 191

a. use a 95% confidence interval to estimate the difference between the population means (u1 - u2). Interpret the confidence interval.

b. test the null hypothesis H0: (u1 - u2) = 0 versus the alternative hypothesis Ha:(u1 - u2) =/ 0. Give the significance level of the test, and interpret the result.

c. Suppose the test in part b was conducted with the alternative hypothsis Ha:(u1 - u2) > 0. How would your answer to part b change?

d. test the null hypothesis H0:(u1 - u2) = 30 versus Ha:(u1 - u2) =/ 30. Give the significance level, and interpret the result. Compare your answer to the test conducted in part b.

e. What assumptions are neccessary to ensure the validity of the inferential procedures applied in parts a - d

Answer 1

Solution :- from the given data, Z as a= 0.05, 2(0.025) = 1.96 (from standard normal table) 80 95% confidence interval is (2 - x2)+/- 25(512/01 +522/12) (5337-5298) +/- 1-96 (1572/385 + 1912/385) = (14.30, 63.70) 2) b) It is a two-tailed = (21-92) test 5337 - 5298 I 1572 1917 385 385 - 3.0951 The P-value = 2xP (2/> 3.095) = 0.00197. Cfrom standard normal table)

c) The P-value would the P-value would be 0.0114, so reject to for a > 0.00197. is: d) The test statistic Z= (XI-X2 - 39) ng - (5337 - 5298) -30) = 0.714 The P-value = 2xP (z >0.714) = 0.4752. (from Standard normal lable) 2) e) we must -pendent random assume that we have two inde- samples.
Thank you.