1. As a result of a prolonged economic boom, Toronto is undergoing several changes that are starting to cause social and economic problems. One serious problem is the lack of affordable housing for young people. Median house prices over a 12-month period in the Toronto area are shown in the table below: Month Price ($K) Month Price ($K) Jan $195 Jul $205 Feb 196 Aug 199 Mar 205 Sep 201 Apr 210 Oct 197 May 212 Nov 192 Jun 210 Dec 190 a) Graph the data in the table. Describe the trend that you see. b) Calculate the mean and standard deviation. c) Calculate the range and mode of these data. d) If $195K is considered the threshold for affordability, can we conclude at the 5 % level of significance that the threshold has increased in this period? 2. We would like to establish the 95% confidence interval for the proportion of left-handed baseball players. We drew a sample of 59 baseball players and found that 15 are lefthanded. Using this estimate, find the 95% confidence interval for true proportion of left-handed players in baseball. a). Compute the estimate b). Compute the standard error c). Compute the margin of error d). Calculate the confidence interval 3. Suppose that the height of a person is normally distributed with a mean of 5’ 9” (69”) and a standard deviation of 2 inches. Find the minimum height of the ceiling of an airplane, such that at most 2 % of the people walking down the aisle will have to duck their heads. a) Define the random variable, i.e., Let X = ? b) Solve the problem. 4. A diet doctor claims that the average American is more than 10 pounds overweight. To test his claim, a random sample of 50 Americans was selected and each weighed, and for each the difference between actual weigh and idea weight was calculated. The mean and standard deviation of that difference was 11.5 and 2.2 pounds respectively. Can we conclude, with = .05, that enough evidence exists to show that the doctor’s claim is true? a) State the Null and Alternative hypotheses. b) Define the test statistic and obtain the critical value. c) Compute the test statistic. d) Make the decision to reject or not reject the null hypothesis e) State the conclusion. 5. A venture capital company feels that the rate of return (X) on a proposed investment is normally distributed with a mean of 30 basis points and a standard deviation of 10 basis points. Find the probability that the return will exceed 55 basis points. a) Define the random variable for this problem b) Write the probability statement for the event c) Solve the problem
