In order to study whether the proportion of left handers among musicians is diff

Question

In order to study whether the proportion of left handers among musicians is different than the proportion among non-musicians, two random samples are taken: one of 9 musicians and one of 44 non-musicians. In the samples, 2 of the musicians and 1 of the non-musicians are left handed, (a) Use a level 0.95 approximate score confidence interval for the differences of the proportions of left handers between musicians (p_1) and non-musicians (p_2): lessthanorequalto p_1-p_2 lessthanorequalto (b) Does the interval suggest that there is a difference in the proportions? A. No B. Yes

Explanation / Answer

A) p1 = 2/9, p2 = 1/44

SEp1-p2 = sqrt{ [p1 * (1 - p1) / n1] + [p2 * (1 - p2) / n2] } = sqrt{[2/9*(1-2/9)/9] + [1/44*(1-1/44)/44]} = 0.0197092

For = 0.05, zcrit = 1.96

lower bound = p1 - p2 - zcrit*SEp1-p2 = 2/9 - 1/44 - 1.96*0.0197092 = 0.16086
upper bound = p1 - p2 + zcrit*SEp1-p2 = 2/9 - 1/44 - 1.96*0.0197092 = 0.23812

0.16086 <= p1 - p2 <= 0.23812

B) Yes, as the confidence interval doesnt contain 0

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