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Chapter 5 #57. There are 100 employees at Kiddie...

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Chapter 5 #57. There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are production workers, 40 are supervisors, 2 are secretaries, and the remaining employee is the president. Suppose an employee is selected: a. What is the probability the selected employee is a production worker? b. What is the probability the selected employee is either a production worker or a supervisor? c. Refer to part (b). Are these events mutually exclusive? d. What is the probability the selected employee is neither a production worker nor a supervisor? Chapter 6 #63. A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 P.M. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find: a. No customers are waiting? b. Four customers are waiting? c. Four or fewer are waiting? d. Four or more are waiting? Chapter 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? Chapter 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? Chapter 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. 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 Chapter 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? Chapter 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? Chapter 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: y= total sales last year (in $ thousands) x1 = number of competitors in the region x2= population in the region(in millions) x3= advertising expense (in $ thousands) The sample data were run on MINITAB, with the following results. 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 R square 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. Chapter 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. 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

 

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