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Week 5 ? Exercises 31, 32, and 38 (Ch. 10) 3...

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Week 5 ? Exercises 31, 32, and 38 (Ch. 10) 31. A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on the average, 10 pounds the first two weeks with a standard deviation of 2.8 pounds. A random sample of 50 people who joined the new weight reduction program revealed the mean loss to be 9 pounds. At the .05 level of significance, can we conclude that those joining Weight Reducers on average will lose less than 10 pounds? Determine the p-value. 32. Dole Pineapple, Inc., is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is .03 ounces. The qualitycontrol department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value 38. A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent): 4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6 Exercises 27, 46, and 52 (Ch. 11) 27- A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below. At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? What is the p-value? Statistic Men Women Sample mean 24.51 22.69 Population standard deviation 4.48 3.86 Sample size 35 40 Exercises 23 and 28 (Ch. 12) 23. A real estate agent in the coastal area of Georgia wants to compare the variation in the selling price of homes on the oceanfront with those one to three blocks from the ocean. A sample of 21 oceanfront homes sold within the last year revealed the standard deviation of the selling prices was $45,600. A sample of 18 homes, also sold within the last year, that were one to three blocks from the ocean revealed that the standard deviation was $21,330. At the .01 significance level, can we conclude that there is more variation in the selling prices of the oceanfront homes? 28. The following is a partial ANOVA table. Discount Variety Department $12 $15 $19 13 17 17 14 14 16 12 18 20 15 17 19 Sum of Mean Source Squares df Square F Treatment 2 Error 20 Total 500 11 Complete the table and answer the following questions. Use the .05 significance level. a. How many treatments are there? b. What is the total sample size? c. What is the critical value of F? d. Write out the null and alternate hypotheses. e. What is your conclusion regarding the null hypothesis? Exercises 19 and 20 (Ch. 17) 19. In a particular market there are three commercial television stations, each with its own evening news program from 6:00 to 6:30 P.M. According to a report in this morning?s local newspaper, a random sample of 150 viewers last night revealed 53 watched the news on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13). At the .05 significance level, is there a difference in the proportion of viewers watching the three channels? 20. There are four entrances to the Government Center Building in downtown Philadelphia. The building maintenance supervisor would like to know if the entrances are equally utilized. To investigate, 400 people were observed entering the building. The number using each entrance is reported below. At the .01 significance level, is there a difference in the use of the four entrances Entrance Frequency Main Street 140 Broad Street 120 Cherry Street 90 Walnut Street 50 Total 400 Week 6 ? Exercise 88 (Ch. 3) 88. Refer to the Baseball 2005 data, which reports information on the 30 major league teams for the 2005 baseball season. a. Select the variable team salary and find the mean, median, and the standard deviation. b. Select the variable that refers to the age the stadium was built. (Hint: Subtract the year in which the stadium was built from the current year to find the stadium age and work with that variable.) Find the mean, median, and the standard deviation. c. Select the variable that refers to the seating capacity of the stadium. Find the mean, median, and the standard deviation ? Exercise 56 (Ch. 5) 56. Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of the scheduled time is .90. We select four flights from yesterday for study. a. What is the likelihood all four of the selected flights arrived within 15 minutes of the scheduled time? b. What is the likelihood that none of the selected flights arrived within 15 minutes of the scheduled time? c. What is the likelihood at least one of the selected flights did not arrive within 15 minutes of the scheduled time? Exercise 64 (Ch. 6) 64. An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution. a. What is the probability Linda Lahey, company president, received exactly 1 email between 4 P.M. and 5 P.M. yesterday? b. What is the probability she received 5 or more email during the same period? c. What is the probability she did not receive any email during the period? ? Exercise 50 (Ch. 7) 50. Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles. a. What percent of the Ford Super Duty F-750s logged 65,200 miles or more? b. What percent of the trucks logged more than 57,060 but less than 58,280 miles? c. What percent of the Fords traveled 62,000 miles or less during the year? d. Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles? Explain. ? Exercise 38 (Ch. 8) 38. The mean amount purchased by a typical customer at Churchill?s Grocery Store is $23.50 with a standard deviation of $5.00. Assume the distribution of amounts purchased follows the normal distribution. For a sample of 50 customers, answer the following questions. a. What is the likelihood the sample mean is at least $25.00? b. What is the likelihood the sample mean is greater than $22.50 but less than $25.00? c. Within what limits will 90 percent of the sample means occur? ? ? ? ? ? ? ? Exercise 54 (Ch. 9) 54. Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000. a. Based on this sample information, develop a 90 percent confidence interval for the population mean yearly premium. b. How large a sample is needed to find the population mean within $250 at 99 percent confidence? ? Exercise 42 (Ch. 10) 42. During recent seasons, Major League Baseball has been criticized for the length of the games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following times to completion. (Note that the minutes have been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes is reported at 2.40 hours.) 2.98 2.40 2.70 2.25 3.23 3.17 2.93 3.18 2.80 2.38 3.75 3.20 3.27 2.52 2.58 4.45 2.45 Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05 significance level ? Exercise 58 (Ch. 11) 58. The amount of income spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes, and utility costs (water, heat, electricity). An economist selected a sample of 20 homeowners in New England and then calculated these total housing costs as a percent of monthly income, five years ago and now. The information is reported below. Is it reasonable to conclude the percent is less now than five years ago? Homeowner Five Years Ago Now Homeowner Five Years Ago Now 1 17% 10% 11 35% 32% 2 20 39 12 16 32 3 29 37 13 23 21 4 43 27 14 33 12 5 36 12 15 44 40 6 43 41 16 44 42 7 45 24 17 28 22 8 19 26 18 29 19 9 49 28 19 39 35 10 49 26 20 22 12 ? Exercise 42 (Ch. 12) 42. Martin Motors has in stock three cars of the same make and model. The president would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial. Distance (miles) Types of Gasoline Car A Car B Car C Regular 22.4 20.8 21.5 Super regular 17.0 19.4 20.7 Unleaded 19.2 20.2 21.2 Premium unleaded 20.3 18.6 20.4 Using the .05 level of significance: a. Is there a difference among types of gasoline? b. Is there a difference in the cars? ? Exercises 37 and 40 (Ch. 13) 37. A regional commuter airline selected a random sample of 25 flights and found that the correlation between the number of passengers and the total weight, in pounds, of luggage stored in the luggage compartment is 0.94. Using the .05 significance level, can we conclude that there is a positive association between the two variables? 40. A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied. Day Income Occupied Day Income Occupied 1 $1,452 23 14 $1,425 27 2 1,361 47 15 1,445 34 3 1,426 21 16 1,439 15 4 1,470 39 17 1,348 19 5 1,456 37 18 1,450 38 6 1,430 29 19 1,431 44 7 1,354 23 20 1,446 47 8 1,442 44 21 1,485 43 9 1,394 45 22 1,405 38 10 1,459 16 23 1,461 51 11 1,399 30 24 1,490 61 12 1,458 42 25 1,426 39 13 1,537 54 Use a statistical software package to answer the following questions. a. Does the breakfast revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion. b. Determine the coefficient of correlation between the two variables. Interpret the value. c. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level. d. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? Exercises 17 and 18 (Ch. 14) 17. The district manager of Jasons, a large discount electronics chain, is investigating why certain stores in her region are performing better than others. She believes that three factors are related to total sales: the number of competitors in the region, the population in the surrounding area, and the amount spent on advertising. From her district, consisting of several hundred stores, she selects a random sample of 30 stores. For each store she gathered the following information. sales last year (in $ thousands). of competitors in the region. of the region (in millions). expense (in $ thousands). The sample data were run on MINITAB, with the following results. X3 _ advertising X2 _ population X1 _ number Y _ total n _ 20, R2. Analysis of variance SOURCE DF SS MS Regression 5 100 20 Error 20 40 2 Total 25 140 Predictor Coef StDev t-ratio Constant 3.00 1.50 2.00 X1 4.00 3.00 1.33 X2 3.00 0.20 15.00 X3 0.20 0.05 4.00 X4 _2.50 1.00 _2.50 X5 3.00 4.00 0.75 Analysis of variance SOURCE DF SS MS Regression 3 3050.00 1016.67 Error 26 2200.00 84.62 Total 29 5250.00 Predictor Coef StDev t-ratio Constant 14.00 7.00 2.00 X1 _1.00 0.70 _1.43 X2 30.00 5.20 5.77 X3 0.20 0.08 2.50 a. What are the estimated sales for the Bryne store, which has four competitors, a regional population of 0.4 (400,000), and advertising expense of 30 ($30,000)? b. Compute the R2 value. c. Compute the multiple standard error of estimate. d. Conduct a global test of hypothesis to determine whether any of the regression coefficients are not equal to zero. Use the .05 level of significance. e. Conduct tests of hypotheses to determine which of the independent variables have significant regression coefficients. Which variables would you consider eliminating? Use the .05 significance level. 18. Suppose that the sales manager of a large automotive parts distributor wants to estimate as early as April the total annual sales of a region. On the basis of regional sales, the total sales for the company can also be estimated. If, based on past experience, it is found that the April estimates of annual sales are reasonably accurate, then in future years the April forecast could be used to revise production schedules and maintain the correct inventory at the retail outlets. Several factors appear to be related to sales, including the number of retail outlets in the region stocking the company?s parts, the number of automobiles in the region registered as of April 1, and the total personal income for the first quarter of the year. Five independent variables were finally selected as being the most important (according to the sales manager). Then the data were gathered for a recent year. The total annual sales for that year for each region were also recorded. Note in the following table that for region 1 there were 1,739 retail outlets stocking the company?s automotive parts, there were 9,270,000 registered automobiles in the region as of April 1 and so on. The sales for that year were $37,702,000 Annual Number of Automobiles Personal Age of Sales Retail Registered Income Automobiles Number of ($ millions), Outlets, (millions), ($ billions), (years), Supervisors, Y X1 X2 X3 X4 X5 37.702 1,739 9.27 85.4 3.5 9.0 24.196 1,221 5.86 60.7 5.0 5.0 32.055 1,846 8.81 68.1 4.4 7.0 3.611 120 3.81 20.2 4.0 5.0 17.625 1,096 10.31 33.8 3.5 7.0 45.919 2,290 11.62 95.1 4.1 13.0 29.600 1,687 8.96 69.3 4.1 15.0 8.114 241 6.28 16.3 5.9 11.0 20.116 649 7.77 34.9 5.5 16.0 12.994 1,427 10.92 15.1 4.1 10.0 a. Consider the following correlation matrix. Which single variable has the strongest correlation with the dependent variable? The correlations between the independent variables outlets and income and between cars and outlets are fairly strong. Could this be a problem? What is this condition called? sales outlets cars income age outlets 0.899 cars 0.605 0.775 income 0.964 0.825 0.409 age _0.323 _0.489 _0.447 _0.349 bosses 0.286 0.183 0.395 0.155 0.291 b. The output for all five variables is on the following page. What percent of the variation is explained by the regression equation? The regression equation is sales _ _19.7 _ 0.00063 outlets _ 1.74 cars _ 0.410 income _ 2.04 age _ 0.034 bosses Predictor Coef StDev t-ratio Constant _19.672 5.422 _3.63 outlets _0.000629 0.002638 _0.24 cars 1.7399 0.5530 3.15 income 0.40994 0.04385 9.35 age 2.0357 0.8779 2.32 bosses _0.0344 0.1880 _0.18 Analysis of Variance SOURCE DF SS MS Regression 5 1593.81 318.76 Error 4 9.08 2.27 Total 9 1602.89 c. Conduct a global test of hypothesis to determine whether any of the regression coefficients are not zero. Use the .05 significance level. d. Conduct a test of hypothesis on each of the independent variables. Would you consider eliminating ?outlets? and ?bosses?? Use the .05 significance level. e. The regression has been rerun below with ?outlets? and ?bosses? eliminated. Compute the coefficient of determination. How much has R2 changed from the previous analysis? The regression equation is sales _ _18.9 _ 1.61 cars _ 0.400 income _ 1.96 age Predictor Coef StDev t-ratio Constant _18.924 3.636 _5.20 cars 1.6129 0.1979 8.15 income 0.40031 0.01569 25.52 age 1.9637 0.5846 3.36 Analysis of Variance SOURCE DF SS MS Regression 3 1593.66 531.22 Error 6 9.23 1.54 Total 9 1602.89 f. Following is a histogram and a stem-and-leaf chart of the residuals. Does the normality assumption appear reasonable? Histogram of residual N _ 10 Stem-and-leaf of residual N _ 10 Leaf Unit _ 0.10 Midpoint Count _1.5 1 * 1 _1 7 _1.0 1 * 2 _1 2 _0.5 2 ** 2 _0 _0.0 2 ** 5 _0 440 0.5 2 ** 5 0 24 1.0 1 * 3 0 68 1.5 1 * 1 1 1 1 7 g. Following is a plot of the fitted values of Y (i.e., and the residuals. Do you see any violations of the assumptions? Exercise 22 (Ch. 17) 22. Banner Mattress and Furniture Company wishes to study the number of credit applications received per day for the last 300 days. The information is reported on the next page. Nonparametric Methods: Chi-Square Applications 665 Number of Credit Frequency Applications (Number of Days) 0 50 1 77 2 81 3 48 4 31 5 or more 13 To interpret, there were 50 days on which no credit applications were received, 77 days on which only one application was received, and so on. Would it be reasonable to conclude that the population distribution is Poisson with a mean of 2.0? Use the .05 significance level. Hint: To find the expected frequencies use the Poisson distribution with a mean of 2.0. Find the probability of exactly one success given a Poisson distribution with a mean of 2.0. Multiply this probability by 300 to find the expected frequency for the number of days in which there was exactly one application. Determine the expected frequency for the other days in a similar manner,Thanks & Happy Holidays, MARIA,Thanks Natalia

 

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