work please! (a) Find the size of each of two samples (assume that they are of e

Question

work please!

(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume the "worst case" scenario for the value of both sample proportions. We want a 99 99 % confidence level and for the error to be smaller than 0.04.

(b) Again find the sample size required, as in part (a), but with the knowledge that a similar student last year found that the proportion of boys afraid of spiders is 0.53 and the proportion of girls afraid of spiders was 0.56.

Explanation / Answer

a) here margin of error =0.04

and for 99.99% CI, z=3.8906

also as estimation not given we assume p1=p2=0.5

hence sample size =(p1(1-p1)+p2(1-p2))(Z/E)2 =~4731

b) for p1=0.53 and p2=0.56

sample size from above formula n=~4688

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