How hard is it to reach a businessperson by phone? Let p be the proportion of ca

Question

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 99% sure that the point estimate p? will be within a distance of 0.056 from p? (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).

Explanation / Answer

Solution:-

a) (a) p = 0.5
margin of error, E = 0.056
z_c = 2.58 at 99% confidence.

n = (z/SE)^2*p*(1-p)

=> n = (2.58/0.056)^2*0.5*(1-0.5)

=> n = 530.6441

=> n = 531

b) p = 0.23

=> n = (2.58/0.056)^2*0.23*(1-0.23)

=> n = 375.9083

n = 376

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