How hard is it to reach a businessperson by phone Let p be t

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 85% sure that the point estimate p? will be within a distance of 0.066 from p?


(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).

Solution

(a) Given a=1-0.85=0.15, Z(0.15/2) = Z(0.075) = 1.44 (from standard normal table)

We use p=0.5 as estimated.

So n=(Z/E)^2*p*(1-p)

=(1.44/0.066)^2*0.5*0.5

=119.0083

Take n=120

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(b)

So n=(Z/E)^2*p*(1-p)

=(1.44/0.066)^2*0.13*(1-0.13)

=53.83934

Take n=54