# Quantitative analysis

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

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