Choose the one alternative that best completes the statement or answers the ques

Question

Choose the one alternative that best completes the statement or answers the question. Suppose you want to test the claim that mu_1 = mu_2. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that sigma^2_1 = sigma^2_2. At a level of significance of alpha = 0.05, when should you reject H_0? n_1 = 14 n_2 = 12 x^bar 1 = 21 x^bar 2 = 22 s_1 = 2.5 s_2 = 2.8 A) Reject H_0 if the standardized test statistic is less than -1.318 or greater than 1.318. B) Reject H_0 if the standardized test statistic is less than -2.492 or greater than 2.492 C) Reject H_0 if the standardized test statistic is less than -2 064 or greater than 2 064 D) Reject H_0 if the standardized test statistic is less than -1.711 or greater than 1.711

Explanation / Answer

given n1 =14

n2 =12

x1 =21

x2= 22

s1=2.5

s2 =2.8

s(x1 - x2) = [(s1²/n1) + (s2²/n2)]

= [(2.5²/14) + (2.8²/12)]

=1.4764

. . x1 - x2
t = ------------------

. . . . s(x1 - x2)
t = (21-22) / 1.4764 = -1.318

so answer is option a

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