In order to compare the means of two populations, independentrandom samples of 4

Question

In order to compare the means of two populations, independentrandom samples of 400 observations are selected from eachpopulation, with the following results:
Sample1                                 Sample 2
xbar1 =5275                           xbar2 = 5240
s1 =150                                   s2 = 200
a. Use a 95% confidence interval to estimate the difference betweenthe population means (1-2). Interpret the confidenceinterval.
b. Test the null hypothesis H0 (1-2) = 0 versus thealternative hypothesis Ha: (1-2) 0. Give thesignificance level of the test, and interpret the result.
c. Suppose the test in part b was conducted with the alternativehypothesis Ha: (1-2) > 0. How would your answer topart b change?
d. Test the null hypothesis H0: (1-2) = 25 versus thealternative Ha: (1-2) 25. Give the significancelevel and interpret the result. Compare your answer to the testconducted in part b.

e. What assumptions are necessary to ensure the validity of theinferential procedures applied in parts a-d?

Explanation / Answer

(a) Given =0.05, |Z(0.025)|=1.96 (check normal table) The 95% CI is (xbar1-xbar2) ± Z*[(s1^2/n1 +s2^2/n2)] --> (5275-5240) ± 1.96*sqrt(150^2/400 + 200^2/400) --> (10.5, 59.5)

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