Basic Statistics for Business and Economics

60. Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22.
a. Compute the mean number and median number of apples in a bag.
b. Verify that _(X _ ) _ 0.

62. The Citizens Banking Company is studying the number of times the ATM located in a Loblaws Supermarket at the foot of Market Street is used per day. Following are the numbers of times the machine was used over each of the last 30 days. Determine the mean number of times the machine was used per day.

83 64 84 76 84 54 75 59 70 61
63 80 84 73 68 52 65 90 52 77
95 36 78 61 59 84 95 47 87 60

68. The American Automobile Association checks the prices of gasoline before many holiday weekends. Listed below are the self-service prices for a sample of 15 retail outlets during the May 2003 Memorial Day weekend in the Detroit, Michigan, area.

1.44 1.42 1.35 1.39 1.49 1.49 1.41 1.46
1.41 1.49 1.45 1.48 1.39 1.46 1.44

70. A recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3 percent per year, you'll need to make $33,598 in 10 years to have the same buying power. You would need to make $44,771 if the inflation rate jumped to 6 percent.
Confirm that these statements are accurate by finding the geometric mean rate of increase.

72. The weights (in pounds) of a sample of five boxes being sent by UPS are: 12, 6, 7, 3, and 10.
a. Compute the range.
b. Compute the mean deviation.
c. Compute the standard deviation.

8. A sample of 2,000 licensed drivers revealed the following number of speeding violations.

Number of Violations Number of Drivers
0 1,910
1 46
2 18
3 12
4 9
5 or more 5
Total 2,000

a. What is the experiment?
b. List one possible event.
c. What is the probability that a particular driver had exactly two speeding violations?
d. What concept of probability does this illustrate?

66. A survey of undergraduate students in the School of Business at Northern University revealed the following regarding the gender and majors of the students:

Major
Gender Accounting Management Finance Total
Male 100 150 50 300
Female 100 50 50 200
Total 200 200 100 500

a. What is the probability of selecting a female student?
b. What is the probability of selecting a finance or accounting major?
c. What is the probability of selecting a female or an accounting major? Which rule of addition did you apply?
d. Are gender and major independent? Why?
e. What is the probability of selecting an accounting major, given that the person selected
is a male?
f. Suppose two students are selected randomly to attend a lunch with the president of the
University. What is the probability that both of those selected are accounting majors?

4. Which of these variables are discrete and which are continuous random variables?
a. The number of new accounts established by a salesperson in a year.
b. The time between customer arrivals to a bank ATM.
c. The number of customers in Big Nick's barber shop.
d. The amount of fuel in your car's gas tank.
e. The number of minorities on a jury.
f. The outside temperature today.

38. The accounting department at Weston Materials, Inc., a national manufacturer of unattached garages, reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution.
a. Determine the z values for 29 and 34 hours. What percent of the garages take between
32 hours and 34 hours to erect?
b. What percent of the garages take between 29 hours and 34 hours to erect?
c. What percent of the garages take 28.7 hours or less to erect?
d. Of the garages, 5 percent take how many hours or more to erect?

44. The number of passengers on the Carnival Sensation during one-week cruises in the
Caribbean follows the normal distribution. The mean number of passengers per cruise is
1,820 and the standard deviation is 120.
a. What percent of the cruises will have between 1,820 and 1,970 passengers?
b. What percent of the cruises will have 1,970 passengers or more?
c. What percent of the cruises will have 1,600 or fewer passengers?
d. How many passengers are on the cruises with the fewest 25 percent of passengers?

60. In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?

12. The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 90 percent confidence interval, what is the value of t?
d. Develop the 90 percent confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 63 pounds?

28. A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation 0.5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than 0.2 pounds?

6. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road
MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

18. The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

24. Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the afternoon shift than on the day shift. A sample of 54 day-shift workers showed that the mean number of units produced was 345, with a standard deviation of 21. A sample of 60 afternoon-shift workers showed that the mean number of units produced was 351, with a standard deviation of 28 units. At the .05 significance level, is the number of units produced on the afternoon shift larger?

38. Two boats, the Prada (Italy) and the Oracle (U.S.A.), are competing for a spot in the upcoming America's Cup race. They race over a part of the course several times. Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?
Boat Times (minutes)
Prada (Italy) 12.9 12.5 11.0 13.3 11.2 11.4 11.6 12.3 14.2 11.3
Oracle (U.S.A.)14.1 14.1 14.2 17.4 15.8 16.7 16.1 13.3 13.4 13.6 10.8 19.0

30. There are four auto body shops in a community and all claim to promptly serve customers. To check if there is any difference in service, customers are randomly selected from each repair shop and their waiting times in days are recorded. The output from a statistical software package is:
Summary
Groups Count Sum Average Variance
Body Shop A 3 15.4 5.133333 0.323333
Body Shop B 4 32 8 1.433333
Body Shop C 5 25.2 5.04 0.748
Body Shop D 4 25.9 6.475 0.595833

12. For many years TV executives used the guideline that 30 percent of the audience were watching each of the prime-time networks and 10 percent were watching cable stations on a weekday night. A random sample of 500 viewers in the Tampa-St. Petersburg, Florida, area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station. At the .05 significance level, can we conclude that the guideline is still reasonable?

26. A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the .01 significance level, is there a relationship between job pressure and age?
Degree of Job Pressure
Age (years) Low Medium High
Less than 25 20 18 22
25 up to 40 50 46 44
40 up to 60 58 63 59
60 and older 34 43 43