Answer the questions below

1) While talking about the cars that fellow students drive, several statements were made about types, ages, makes, colors, and so on. Dana decided she wanted to estimate the proportion of convertibles students drove, so he randomly identified 200 cars in the student parking lot, of which he found 17 to be convertibles. a) Find the 90% confidence interval for the proportion of convertibles driven by students. Check conditions. Include the sample proportion, Z/2 and standard error followed by your confidence interval. Then state your confidence interval in words. b) What is the margin of error? ___________. c) What sample size would be required to reduce the margin of error to 1%? ___________ 2) While talking about the cars that fellow students drive, Tom made the claim that 15% of the students drive convertibles. Test the claim using Dana's sample data given above. Is there significant evidence at the 2% level to reject Tom's claim? State the hypotheses, compute the test statistic, standardize, make a sketch, compute the p-value, state your conclusions followed by a summary statement. (Checking conditions was done in problem 1).