Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

How hard is it to reach a businessperson by phone? Let p be the proportion of calls to businesspeople for which the caller reaches the person being called on the first try.

(a) If you have no preliminary estimate for p, how many business phone calls should you include in a random sample to be 80% sure that the point estimate p̂ will be within a distance of 0.05 from p? (Round your answer up to the nearest whole number.)
phone calls

(b) A report states that businesspeople can be reached by a single phone call approximately 13% of the time. Using this (national) estimate for p, answer part (a). (Round your answer up to the nearest whole number.)
phone calls

Answer 1

(a)

If you have no preliminary estimate for p, we can assume p = 0.50 to have conservative estimate of the sample size.

Z value of 80% confidence interval is 1.28

Margin of Error, E = 0.05

Sample size, n = (z/ E)^2 * p(1-p)

= (1.28 / 0.05)^2 * 0.5 * (1 - 0.5)

= 164 (Rounded to nearest whole number)

(b)

Given, p = 0.13

Z value of 80% confidence interval is 1.28

Margin of Error, E = 0.05

Sample size, n = (z/ E)^2 * p(1-p)

= (1.28 / 0.05)^2 * 0.13 * (1 - 0.13)

= 74 (Rounded to nearest whole number)