Suppose you want to estimate the proportion of people in your community who woul

Question

Suppose you want to estimate the proportion of people in your community who would choose Thin Mints as their favorite Girl Scout cookie. Also suppose previous studies have shown this proportion to be around .4 .

a. Determine how many people you would have to sample in order to estimate this proportion to within .025 with 95% confidence.

If your boss says that this number (your answer to part a) is too large to be practical, you might respond that a smaller sample size would suffice if either the margin-of-error (.025) or the confidence level (95%) were changed.

b. In which direction would the margin-of-error need to change in order for a smaller sample size to suffice?

c. In which direction would the confidence level need to change in order for a smaller sample size to suffice?

Explanation / Answer

a) Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)

Z a/2 at 0.05 is = 1.96

Sample Proportion = 0.4

ME = 0.025

n = ( 1.96 / 0.025 )^2 * 0.4*0.6

= 1475.1744 ~ 1476                           

b. margin-of-error need to increased to change in order for a smaller sample size

c. Decrease the confidence level direction would change in order for a smaller sample size

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