A researcher is interested in determining the proportion of first year universit

Question

A researcher is interested in determining the proportion of first year university students who have suffered hearing loss from loud music and other big-city sounds. How many students should she give hearing tests to in order to determine this proportion with a margin of error (half width of confidence interval) of 0.12 using a 95% confidence interval? a.) If she believes from previous studies that the true proportion is 0.25. (Give answer as a whole number ) b.) If she has no idea of the proportion with hearing loss. (Give answer as a whole number.)

Explanation / Answer

a) here p=0.25

and for 95% CI, z=1.96

margin of error E=0.12

hence sample size =p(1-p)*(z/E)2 =~51

b) for no idea p=0.5

hence sample size =~67

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