Sample Test #3 Statisitics Do large sample problems with pencil and paper and small sample problems with calculator. 1) You wish to know the average price of buying a certain size tire so you go out and take the random sample below. Use the data below to find a 93% confidence interval for the average price of all tires this size. Find x-bar and s and interpret your results. All data is in dollars. (Use you calculator only. Show no work.) 22.35 24.00 27.27 20.37 30.00 23.56 20.54 24.12 27.40 21.67 19.45 23.65 2) Looking at a sample of 100 USA students, we find the mean GPA of 2.9 with a standard deviation of 0.23. Find an 85% confidence interval for the mean of the whole population of USA students. (2.867, 2.933) 3) From a random sample of 125 eligible voters in Louisiana, we find that 58 voters call themselves a Republican. Find a confidence interval at the 13% significance level for the percent of Republicans in Louisiana. Consider that there are only two parties. (.3965, .5315) 4) A sample of 14 USA students takes an average of 23 minutes to register for classes with a standard deviation of 4.1 minutes. We know these times are normally distributed. Find a 90% confidence interval for 5) You do a study of 500 bears and measure their right paws. You get a mean of 12.8 inches and a standard deviation of 3.56 inches. Use your study to test the claim that the population mean of right bear paws is really 13.1 inches—you , by the way, think it’s less. Use a 6% level of significance. (Reject H0, TS = -1.88 sd, p-value = .0298) 6) It is claimed that the number of people who own red cars is 41%. You think it’s different than 41% so you do your own study and use a simple random sample of 140 car owners. You find that 60 of them own red cars. Use a hypothesis test and a 9% level of significance to test the 41% claim. (TS = .447 sd, p-value = .6550, fail to reject H0) 7) It is claimed that the number of people who own blue cars is 30%. You think it’s more than 30% so you do your own study and use a simple random sample of 90 car owners. You find that 35 of them own blue cars. Use a hypothesis test and a .04 level of significance to test the 30% claim. (TS = 1.84 sd, p-value - .0329, reject H0) 8) In #6 if you rejected H0 and 41% is really the true proportion, you would be making a type ________________________ error. If you fail to reject the 41% in #6 and 41% is not the true proportion, you would making a ___________________ error.