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 p̂will be within a distance of 0.04 from p? (Round your answer up to the nearest whole number.)
257 phone calls.

(b) A report states that businesspeople can be reached by a single phone call approximately 16% of the time. Using this (national) estimate for p, answer part (a). (Round your answer up to the nearest whole number.)

Answer 1

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.04

At 80% confidence level

= 1 - 80%  

= 1 - 0.80 =0.20

/2 = 0.10

Z/2 = Z0.10  = 1.282

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.282 / 0.04)2 * 0.5 * 0.5

= 256.80

sample size = n = 257

b) = 0.16

1 - = 1 - 0.16 = 0.84

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.282 / 0.04)2 * 0.16 * 0.84

= 138.05

sample size = n = 139