Question

A marketing manager is interested in how popular radio is for commuters. In a random sample of 1341 commuters in Columbus, OH, 831 stated they listen to the radio while commuting to work. (a) Find the 90% confidence interval for the proportion of all Franklin County residents who listen to the radio while commuting to work. Interpret this confidence interval in the context of the data. (b) Find the 95% confidence interval for the proportion of all Franklin County residents who listen to the radio while commuting to work. Interpret this confidence interval in the context of the data. (c) Find the 99% confidence interval for the proportion of all Franklin County residents who listen to the radio while commuting to work. Interpret this confidence interval in the context of the data. (d) Based upon your three confidence intervals above, do the sample data suggest that at least 55% of all Franklin County residents listen to the radio while commuting to work? Explain. (e)  Using the sample proportion from this problem scenario, calculate the sample size needed to obtain a 90% confidence interval with a width of 0.02.

Answer 1

Here

a. For 90% CI z value is 1.645 as P(-1.645<z<1.645)=0.90

So Margin of ERror is

Hence CI is

b. For 95% CI z value is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of ERror is

Hence CI is

c. For 99% CI z value is 2.576 as P(-2.576<z<2.576)=0.99

So Margin of ERror is

Hence CI is

d. AS 0.55 is not in the range so the sample data do not suggest that at least 55% of all Franklin County residents listen to the radio while commuting to work.

e.