Reference no: EM132177415
STATS Homework -
Please solve the problems using Minitab as the tool. For each problem, present the results in a non-statistical executive summary as detailed in the document "Instructions-for-Completing-Case-Assignments."
1. The Square Wheel Tire Company has determined that their tires must average 36 inches in diameter in order to fit most car models. A random sample of 100 tires revealed a mean of 36.4 inches with a standard deviation of 2.1 inches. Do you think management has anything to worry about? Use Alpha = 0.05.
2. A new production control assistant is hired by Wong's Cookie Factory. He has promised to increase production to a least 17,000 cookies a day. If he does not, he has promised to quit. After 90 days on the job, output has averaged 16,714.3 cookies, with a standard deviation of 8,012 cookies. At the 10 percent significance level, must he now resign as the new assistant in production control?
3. Tensions between workers and management in a small electrical fine outside Chicago were discussed in a recent issue of Fortune. To combat unionization efforts, the company collected data on 16 firms that had a union structure and found the standard deviation in the length of electrical wire made to certain specifications to be 3.7 inches. Fifteen firms in which no union existed revealed a standard deviation of 2.4 inches. Management claimed that this was evidence that unionization often leads to failure to maintain standards. At the 10 percent significance level, do these statistics support management's claim?
4. A major distillery for alcoholic beverages is interested in gaining a large share of the market composed of people aged 18-23 (in those states where 18 is the legal drinking age). Beer and wine are the traditional favorites of this age group. However, Bill Schuessler, the firm's marketing manager, and Carol Pringle, manager of research and development, feel that a new version of distilled apple cider will appeal to this younger market. While they are sure that the alcohol content should remain below 5 percent, they are not sure exactly what it should be. Therefore, five versions of the cider have been prepared, and each version has been tasted by a random sample of 25 young consumers. Each consumer has evaluated the drink on a 100-point scale, with the higher scores representing a greater liking for the product. The results of the test appear below. What should Schuessler and Pringle conclude?
|
Version
|
|
1%
|
2%
|
3%
|
4%
|
5%
|
|
16
|
40
|
81
|
89
|
53
|
|
18
|
62
|
81
|
95
|
20
|
|
72
|
11
|
35
|
10
|
98
|
|
57
|
49
|
16
|
70
|
67
|
|
30
|
40
|
83
|
94
|
92
|
|
16
|
63
|
35
|
06
|
08
|
|
96
|
77
|
20
|
20
|
59
|
|
39
|
93
|
64
|
20
|
49
|
|
31
|
62
|
76
|
38
|
03
|
|
78
|
91
|
19
|
47
|
32
|
|
03
|
93
|
33
|
30
|
47
|
|
74
|
42
|
33
|
28
|
72
|
|
09
|
06
|
09
|
90
|
95
|
|
42
|
23
|
12
|
42
|
25
|
|
16
|
15
|
08
|
02
|
04
|
|
21
|
45
|
40
|
74
|
20
|
|
21
|
58
|
57
|
80
|
50
|
|
56
|
61
|
78
|
95
|
97
|
|
45
|
65
|
66
|
99
|
24
|
|
91
|
34
|
84
|
98
|
49
|
|
91
|
22
|
21
|
20
|
35
|
|
50
|
07
|
38
|
14
|
21
|
|
65
|
39
|
05
|
22
|
58
|
|
27
|
50
|
96
|
13
|
44
|
|
37
|
16
|
94
|
85
|
17
|
5. Meier and Frank is a chain of department stores located in the Northwest. The company has issued its own credit cards for a number of years. As a new employee in the finance department, imagine that you have been assigned to a major investigation of the firm's credit policies designed to reduce bad debt losses. You are requested to investigate the relationship between marital status at the time the card is issued and the subsequent payment record of the individual.
You randomly select 100 credit cards issued three years previously. Of the 70 individuals who were married at the time the cards were issued, 11 have defaulted on a payment. Of the 30 individuals who were single when the cards were issued, 7 have defaulted. Do these data present sufficient evidence to indicate that marital status affects creditworthiness? Use Alpha = 0.05.
6. Morning House is a mail-order fine that carries a wide range of rather expensive art objects for homes and offices. It operates by advertising a particular item, either in selected magazines or in a direct-mail program. Suppose the sales response varies widely by item, and the firm's management has been unable to predict in advance which items will sell well and which will not. Consequently the firm frequently experiences either stock-outs or excessive inventories. For many of the products Morning House sells, it is possible to order a limited amount for inventory and to place a subsequent order for delivery within two weeks. Thus, if the firm could make an early prediction of the ultimate sales of a product, its inventory problems would be greatly reduced. Since it takes approximately six weeks to receive 90% of the response to a given campaign, an accurate prediction of total sales made as late as the end of the first week of receiving orders would be useful.
The first week's sales and total sales of the last 12 campaigns of the firm are shown below. Can the first week's sales be used to predict total sales?
|
Campaign
|
First week's Sales
|
Total Sales
|
|
1
|
32
|
167
|
|
2
|
20
|
91
|
|
3
|
114
|
560
|
|
4
|
66
|
335
|
|
5
|
18
|
70
|
|
6
|
125
|
650
|
|
7
|
83
|
401
|
|
8
|
65
|
320
|
|
9
|
94
|
470
|
|
10
|
5
|
15
|
|
11
|
39
|
210
|
|
12
|
50
|
265
|
7. The National Restaurant Association is interested in determining if there is a relationship between the type of pizza pie that Americans prefer and the region of the country in which they live. The association randomly selects 285 Americans and records the category of pizza pie that best describes their preference and the region of the country in which they live. The results are as follows:
|
Type of Pizza Pie Preferred
|
Region
|
|
North
|
South
|
East
|
West
|
|
Thin Crust
|
40
|
30
|
35
|
45
|
|
Thick Crust
|
17
|
15
|
21
|
22
|
|
Pan Pizza
|
15
|
15
|
15
|
15
|
At α = .10, what can the Association conclude?