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 0.04 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 callsFor 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 0.04 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) Margin of error,

Given,

E=0.04

80% confidence is asked, so we need to take Z-value for 80% confidence.

Z=1.28

Since, we do not have preliminary estimate for p, assume p=0.5

Substituting in (1) we get,

Solving this,

(b) Given, business people can be reached by a single phone call approximately 13% of the time

Thus p=0.13

(1-p)=0.87

Margin of error,

E=0.04

Z=1.28(Z value for 80% confidence)

Substituting in (1) we get

Solving this,

Same questions are being asked twice.Hence solved only once