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(1.) (TCO B) The following table gives the number of visits to recreational facilities by kind and geographical region. East South Midwest West Totals Local Park 55 328 29 52 464 National Park 233 514 204 251 1202 State Park 100 526 65 102 793 Totals 388 1368 298 405 2459 (A) Referring to the above table, if a visitor is chosen at random, what is the probability that he or she is either from the South or from the West? (15 points) (B) Referring to the above table, given that the visitor is from the Midwest, what is the probability that he or she visited a Local Park? (15 points) (Points: 30) (2). (TCO B and F) The length of time Americans exercise each week is normally distributed with a mean of 15.8 minutes and a standard deviation of 2.2 minutes X P(X < x) P(X > x) Mean Std dev 11 .0146 .9854 15.8 2.2 15 .3581 .6419 15.8 2.2 21 .9910 .0090 15.8 2.2 24 .9999 .0001 15.8 2.2 p(lower) p(upper) (A) Analyze the output above to determine what percentage of Americans will exercise between 11 and 21 minutes per week. (15 points) (B) What percentage of Americans will exercise less than 15 minutes? If 1000 Americans were evaluated, how many would you expect to have exercised less than 15 minutes? (15 points) (Points: 30) (3.) (TCO C) A random sample a 16 Google mangers yield the following information on annual salaries. The sample mean is $79,000, with a sample standard deviation of $6,000. What is the mean salary of all Google managers? What is the 95% confidence interval for the population mean? Confidence interval - mean 95% confidence level 79000 mean 6000 std. dev. 16 n 2.131 t (df = 15) 3197.174 half-width 82197.174 upper confidence limit 75802.826 lower confidence limit (Points: 20) (4.) (TCO E and F) Accu-Copiers, Inc. sells and services the Accu-500 copying machine. As part of its standard service contract, the company agrees to perform routine service on this copier. To obtain information about the time it takes to perform routine service, Accu-Copiers has collected data for 11 service calls. The service calls information revealed the following: Refer to the MegaStat output below to answer questions A through G. (A) Analyze the above output to determine the regression equation. (10 points) (B) What conclusions are possible using the meaning of b0 (intercept) and b1 (regression coefficient) in this problem? (That is, explain the meaning of the coefficients.) (10 points) (C) What conclusions are possible using the coefficient of determination (r-squared)? (6 points) (D) Calculate the coefficient of correlation. Interpret this value. (6 points) (E) Does this data provide significant evidence (a=0.05) that the time to perform routine services is associated with the number of copiers serviced? Find the p-value and interpret. (6 points) (F) Predict the average number of minutes required to service four copiers. (6 points) (G) What is the 95% confidence interval for the number of minutes required for four copiers requiring service? What conclusion is possible using this interval? (6 points) (Points: 50) (5.) (TCO E and F) The U.S. Navy selected 16 hospitals that it believes to be efficiently run and conducted a regression analysis to evaluate the performance of its hospitals in terms of how many labor hours are used relative to how many labor hours are needed. The variables assigned for this analysis are: y = monthly labor hours required x1 = monthly X-ray exposures x2 = monthly occupied bed days (a hospital has one occupied bed day if one bed is occupied for an entire day) x3= average length of patients’ stay (in days) Refer to the MegaStat output below to answer these questions A through D. (A) Analyze the above output to determine the multiple regression equation. (10 points) (B) What conclusions are possible using the result of the global usefulness test (F test)? (10 points) (C) What conclusions are possible using the results of the t-tests of the independent variables (alpha = 0.05). Does this data provide significant evidence (alpha = 0.05) that the monthly labor hours required is associated with monthly X-ray exposures and/or monthly occupied bed days and/or average length of patients’ stay (in days)? Find the p-values and interpret. (10 points) (D) Using the table, predict the monthly labor hours required when the X-ray exposures are 56,194, the bed days are 14,077.88, and the average length of patients’ stay is 6.89. (10 points) (Points: 40) 4. (TCO E and F) Accu-Copiers, Inc. sells and services the Accu-500 copying machine. As part of its standard service contract, the company agrees to perform routine service on this copier. To obtain information about the time it takes to perform routine service, Accu-Copiers has collected data for 11 service calls. The service calls information revealed the following: Refer to the MegaStat output below to answer questions A through G. (A) Analyze the above output to determine the regression equation. (10 points) (B) What conclusions are possible using the meaning of b0 (intercept) and b1 (regression coefficient) in this problem? (That is, explain the meaning of the coefficients.) (10 points) (C) What conclusions are possible using the coefficient of determination (r-squared)? (6 points) (D) Calculate the coefficient of correlation. Interpret this value. (6 points) (E) Does this data provide significant evidence (a=0.05) that the time to perform routine services is associated with the number of copiers serviced? Find the p-value and interpret. (6 points) (F) Predict the average number of minutes required to service four copiers. (6 points) (G) What is the 95% confidence interval for the number of minutes required for four copiers requiring service? What conclusion is possible using this interval? (6 points) (Points: 50)