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 prelimiary estimate for p, how many business phone calls should you include in a random sample to be 95% sure that the point estimate p(hat) will be within a distance of 0.034 from p?

b) A report states that businesspeople can be reached by a single phone call approximately 18% of the time. Using this (national) estimate for p, answer part (a).

Explanation / Answer

a. Here as p is not given we take p=0.5

Now z value is 1.96 as P(-1.96<z<1.96)=0.95

E=0.034

Now formula of E=z*SE(p)=z*sqrt(p(1-p)/n)

So n=z^2*p*(1-p)/E^2=830.8=831

b. Now p=0.18

So n=z^2*p*(1-p)/E^2=1.96^2*0.18*0.82/(0.034^2)=490.5=491

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