For this problem, carry at least four digits after the decimal in your calculati

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 p will be within a distance of 0.05from 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 23% of the time. Using this (national) estimate for p, answer part (a). (Round your answer up to the nearest whole number.)
phone calls

Explanation / Answer

(a) p = 0.5
n = ?

margin of error, E = 0.05
z_c = 1.28 at 80% confidence.

E = sqrt(pq/n)*z_c
or, 0.05 = sqrt(0.5*0.5/n)*1.28
or, n = (0.5*1.28/0.05)^2 = 163.84 = 164

Hope this will be helpful. Thanks and god Bless you ;-)

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