Question

(1 point)

(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% confidence level and for the error to be smaller than 0.02. Answer:

(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 0.51 and the proportion of girls afraid of spiders was 0.82. Answe

Answer 1

(a) Assume that they are of equal size, let the sample size be =n

Margin of Error (M.E.) < 0.02

As, nothing is specified in the question, we assume that the proportion of boys and girls are equally likely. i.e, p= 1/2

Zα/2 = the critical value of the Normal distribution at α/2. Here α = 0.01 (as We want a 99% confidence level)

So, Zα/2 = 2.58

Since, the error should be smller than 0.02 then the sample size would be greater than calculated n.

Ans: the required sample size should be 4161 samples for boys and girls each.

(b) Let us assume the required sample size for boys = n1

and the required sample size for girls = n2

As, specified in the question, the proportion of boys afraid of spider (p1) =0.51

and  the proportion of girls afraid of spider (p2) =0.82

Margin of Error (M.E.) < 0.02

Zα/2 = the critical value of the Normal distribution at α/2. Here α = 0.01 (as We want a 99% confidence level)

So, Zα/2 = 2.58

Since, the error should be smller than 0.02 then the sample size would be greater than calculated n1 and n2

Ans: the required sample size for boys should be 4159

and the required sample size for girls should be 2456