Independent random samples, each containing 70 observations, were selected from
ID: 3224483 • Letter: I
Question
Independent random samples, each containing 70 observations, were selected from two populations. The samples from populations 1 and 2 produced 23 and 11 successes, respectively. Test H_0: (p_1 - p_2) = 0 against H_a: (p_1 - p_2) > 0 Use alpha = 0.02 (a) The test statistic is (b)The P-value is (c) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that (p_1 - p_2) = 0. B. We can reject the null hypothesis that (p1 - p_2) = 0 and accept that (p_1 - p_2) > 0.Explanation / Answer
a)
p1 = 23/70 = 0.329 , n1 = 70 , p2 = 11/70 = 0.157, n2 = 70
p = (p1 * n1 + p2 * n2) / (n1 + n2)
= [(0.329 * 70) + (0.157 * 70)] / (70 + 70)
= 0.243
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = sqrt [ 0.243 * 0.757 * ( 1/70 + 1/70 ) ]
= sqrt [0.003733] = 0.072
z = (p1 - p2) / SE
= (0.329 - 0.157) / 0.072
= 2.39
b) Now, we need to find p value using z = 2.39
p value = 0.008424.
c) we can reject the null hypothesis