Minitab Projects (12 problems)

Five sections of AMDS 8437 took a test in July. The scores are provided in the data file that accompanies this test, with sections identified as A, B, C, D, E.

a. Determine whether the mean grades in the sections might be equal; if they are not equal, determine which one(s) is different. Show all steps in the test(s) that you do. Use a 5% level of significance for your test.

b. What assumptions underlie the test(s) that you performed? Do you think the data satisfy those assumptions? Do you think the test is valid?

Are some unskilled office jobs viewed as having more status than others? Suppose a study is conducted in which eight unskilled, unemployed people are interviewed. The people are asked to rate each of the five positions on a scale from 1 to 10 to indicate the status of the position, with 10 denoting most status and 1 denoting least status. The resulting data are given here. Use α = 0.05 and analyze the data

Five sections of AMDS 8437 took a test in July. The scores are provided in the data file that accompanies this test, with sections identified as A, B, C, D, E.

a. Determine whether the mean grades in the sections might be equal; if they are not equal, determine which one(s) is different. Show all steps in the test(s) that you do. Use a 5% level of significance for your test.

b. What assumptions underlie the test(s) that you performed? Do you think the data satisfy those assumptions? Do you think the test is valid?

A shoe retailer conducted a study to determine whether there is a difference in the number of pairs of shoes sold per day by stores according to the number of competitors within a 1-mile radius and the location of the store. The company researchers selected three types of stores for consideration in the study: stand-alone suburban stores, mall stores, and downtown stores. These stores vary in the numbers of competing stores within a 1-mile radius, which have been reduced to four categories: 0 competitors, 1 competitor, 2 competitors, and 3 or more competitors. Suppose the following data represent the number of pairs of shoes sold per day for each of these types of stores with the given number of competitors. Use α = 0.05 and analyze the data.

Use Minitab to construct side-by-side boxplots for the yarnstrength.txt data . This can be accomplished by placing all the yarn-strength values in one column, with a second column providing numeric codes (1, 2, 3) to specify the draw ratio treatment group. Then, in the boxplot dialog box, specify the grouping variable name in the appropriate place (you may have to experiment a bit). Label your plot well (e.g. don’t use 1, 2, 3 for the draw ratio trt labels).

Yarnstrength.txt

Three treatments on yarn, with corresponding 

yarn strengths Y (pounds). time order unavailable. 

TRT 1 corresponds to the 

currently-used setting for Draw Ratio (a control 

variable). TRT2 has a 5% increase, and TRT 3 a 

10% increase, in DR.

TRT Y
1 19.56 
1 23.71
1 17.70
1 18.75
1 16.28
1 19.89
1 20.46
1 15.33
1 19.23
1 16.65
1 21.95
1 15.78
2 23.16
2 22.94
2 22.32
2 23.24
2 22.29
2 20.42
2 19.28
2 23.02
2 24.41
2 22.69
2 18.96
2 24.65
3 29.72
3 27.51
3 25.06
3 23.54
3 28.09
3 18.53
3 23.98
3 24.97
3 22.44
3 24.94
3 24.19
3 21.49
  

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An experimenter sought to find a “natural” fly repellent. Her basic observation consisted of isolating 20 houseflies in a jar whose lid was either (1) untreated cloth (the control treatment) or (2) cloth treated with a solution made with black pepper. After a fixed time, the number of repelled flies (beyond a fixed distance from the lid) out of 20 was counted. This was repeated ten times for each group, and these counts averaged to produce a single Y value for the group under the treatment.

This basic experiment was performed independently with 14 randomly selected groups of flies, seven groups randomly assigned to each treatment, in completely random order. The data are shown below:

Average number of repelled flies (of 20): 14 groups.

Trt1 Trt2

a) (10) Should these samples be considered to be independent of one another? Justify your answer in a sentence or two. It is an important decision, hence the point value.

b) (10) Let m₁ be the long-run mean number of repelled flies for treatment 1 over many tested groups; similarly define m₂ for treatment 2. Which of the methods discussed in class would you use for inference (confidence intervals or hypothesis tests) on m₁-m₂? Justify your answer (NOTE: no need for any printouts here; if you make a plot, tell me what plot you made, and tell me what you see in the plot. If you do a formal test, tell me what test you did and tell me how it turned out, including the P-value).

c) (10) Using the method you selected and justified in parts (a) and (b), obtain and interpret (in widely understandable language) a 95% confidence interval for m₁-m₂.

d) (10) Is there strong evidence here that the black-pepper solution has a higher long-run average number of repelled flies than the untreated cloth? Test appropriate hypotheses using the method you selected and justified in parts (a) and (b). Give the hypotheses in terms of m₁ and m₂, the test statistic, the P-value, and an interpretation in widely understandable language.

A sample of 10 international telephone calls provided the Sprint and WorldCom calling rates per minute for calls from the United States (World Traveler, July 2000)

Provide a 95% confidence interval estimate of the difference between the two population means.

For the data set rainfall.txt use Minitab to construct a well-labeled histogram for the unseeded rainfall amounts, which are in units of acre-feet. How would you describe this distribution? Repeat this using the logarithms base-10 of the rainfall amounts (hint: compute these using the Calc menu in MTB).

Rainfall.txt

Row unseeded seeded

 1 1202.60 2745.60

 2 830.10 1697.80

 3 372.40 1656.00

 4 345.50 978.00

 5 321.20 703.40

 6 244.30 489.10

 7 163.00 430.00

  8 147.80 334.10

 9 95.00 302.80

 10 87.00 274.70

 11 81.20 274.70

 12 68.50 255.00

 13 47.30 242.50

 14 41.10 200.70

 15 36.60 198.60

 16 29.00 129.60

 17 28.60 119.00

 18 26.30 118.30

 19  26.10 115.30

 20 24.40 92.40

 21 21.70 40.60

 22 17.30 32.70

 23 11.50 31.40

 24 4.90 17.50

 25 4.90 7.70

 26 1.00 4.10

Prof. Bumble is a statistics professor at a large private university in FL. He often forgets where he has parked his car and has to be escorted there by the university security staff. He has been there a long time and Dr. Jekyll of the medical staff has noticed that as Prof. Bumble gets older the number of times he loses his car increases. Dr. Jekyll has collected the following data from security records.

Prof. Bumble’s age # times looses car/year

42 7

43 6

44 5

45 12

46 10

47 16

48 17

49 14

50 21

51 19

52 24

53 22

54 30

55 29

56 34

57 33

58 41

59 42

60 38

a) Is Professor Bumble getting more forgetful with age?

b) What would the prediction be for times forgetting his car that you would make should Prof. Bumble continue to 70 years old?

c) Would the prediction in b) be valid? Why or why not?

d) How much of the variance in times losing car can be accounted for by his age?

A company sets different prices for a pool table in eight different regions of the country. The accompanying table shows the numbers of units sold and the corresponding prices (in hundreds of dollars).

1. Plot these data, and estimate the linear regression to express sales in terms of price.
2. What effect would you expect a $150 increase in price to have on sales? Please provide a number as your answer.

BZ Mining, Inc., has five large pumps that pump water from the mines it operates. Management has been concerned lately about the amount of money required to repair malfunctioning pumps. These costs are sums over and above the amounts spent for routine maintenance. To get a better idea of the relationship between these costs and other factors connected with the pumps, the operations superintendent wants to run a regression analysis relating the variables shown in the accompanying table. Find the predicted mean monthly repair cost for a pump of this type that averaged 20 hours of operation per week and was 10 months old at the first of the year.

3. The chief executive officer for Floor Covering Mills, Inc., wants to develop a regression model to predict the monthly profit of the company (in thousands of dollars) from the units of the product that the firm produces (in thousands of units). Data were collected for 15 months when the production level was varied and are presented in the accompanying table. Apparently, if the production level is too high, the amount of inventory increases and the profits decrease.

1. Find the estimated regression equation. Which type of regression model did you use?
2. Predict the profit level for a production level of 5000 (5.0 in our units).

3. Plot the estimated profit equation, and from the plot, determine the production level that maximizes profit.