1) A cruise firm is exploring the possibility of offering a ferry service between Pamban Island and Mannar Island, provided there is sufficient demand to make it feasible. The firm randomly interviewed 210 commuters from the two islands, and 146 of them indicated they would patronize the ferry service instead of the current air taxi service. Estimate the population proportion p of commuters from the two islands who would prefer the ferry service. Construct a 95% confidence interval for p.
2) A firm manufacturing microchips purchases electronic chips from a supplier who claims that his chips are defective only 5% of the time. Determine the sample size that would be required to estimate the true proportion of defective chips if we wanted our estimate, p^, to be within 1.25% of the true proportion, with 99% confidence.
3) More than 80% of retired Italians say that spending time with family and friends is their primary activity. However, approximately 50% say that they travel extensively. Suppose a researcher studying the habits of retired Italians believes that the percentage of retired Italians under the age of 80 who do extensive travelling is greater than 50%. The researcher finds that 40 out of 75 randomly sampled Italians under the age of 80 do extensive travelling. Test the researcher's belief using a significance level of 5%.
4) Test the hypothesis that more female teenagers use twitter than male teenagers. Samples of 500 female and 500 male teenagers were selected, and 430 females and 390 males used twitter in the past week. Use a 10% significance level.