A survey conducted by a travel agency has revealed that within a random sample of 50 interviewed travelers, only 15 of them book their flights on internet. a. Estimate the population proportion of travelers p that have the aforementioned character ristic and compute a 95% confidence interval. b. Let us assume that the point estimate of the population proportion p remains fixed for a new random sample with size different from 50, how large should n be in order that the length of a 95% confidence interval is less than 0.1? c. In a second survey, out of 100 travelers, 32 people booked the flights online. Conduct an hypothesis test with significance level o = 0.05 to determine if the population proportions are the same for the two surveys. (Hint: Use the normal approximation for large samples with the known variances of = pi(1 - p1) and 2 - pz(1 - pz).)