# Inferences About Population Variances: Case Problem Air Force Training Program

Prior to beginning work on this discussion forum, watch the

Week 3 Introductioninks to an external site.

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video, and read Chapter 11 in the MindTap ebook by clicking on the Getting Ready link for each perspective chapter.

Review

Case Problem 1: Air Force Training Program

from Chapter 11 of the ebook.

Step 2: Do:

Run the F-Test Two-Sample for Variances for the Data File Training (Chapter 11) using the video

How to Add Excel’s Data Analysis ToolPakinks to an external site.

for assistance.

In a managerial report,

Use appropriate descriptive statistics to summarize the training time data for each method. What similarities or differences do you observe from the sample data?

Compute the standard deviation and variance for each training method. Conduct a hypothesis test about the equality of population variances for the two training methods. Clearly state the null and alternative hypothesis and analyze the p-value. State your conclusion.

Explain what conclusion you can reach about any differences between the two methods. What is your recommendation? Explain.

• Suggest other data or testing that might be desirable before making a final decision on the training program to be used in the future.
• Step 3: Discuss:

What did you find in your analysis of the data? Were there any surprising results? What recommendations would you make based on your findings? Include details from your managerial report to support your recommendations.

Case Problem Par, Inc.
Par, Inc., is a major manufacturer of golf equipment.
Management believes that Par’s market share could be
increased with the introduction of a cut-resistant, longer-lasting
golf ball. Therefore, the research group at Par has been
investigating a new golf ball coating designed to resist cuts and
provide a more durable ball. The tests with the coating have
been promising.
One of the researchers voiced concern about the effect of the
new coating on driving distances. Par would like the new cutresistant ball to offer driving distances comparable to those of
the current-model golf ball. To compare the driving distances
for the two balls, 40 balls of both the new and current models
were subjected to distance tests. The testing was performed
with a mechanical hitting machine so that any difference
between the mean distances for the two models could be
attributed to a difference in the two models. Theresults of the
tests, with distances measured to the nearest yard, follow.
These data are available in the file Golf.
Model
Current
New
264
277
261
269
267
263
272
266
258
262
283
251
258
262
266
289
Model
Current
New
259
286
270
264
270
272
287
259
289
264
280
280
272
274
275
281
265
276
260
269
278
268
275
262
263
274
264
266
284
262
263
271
260
260
283
281
255
250
272
263
266
278
268
264
281
283
274
250
273
253
263
260
Model
Current
New
275
270
267
263
279
261
274
255
276
263
262
279
Managerial Report
1. Formulate and present the rationale for
a hypothesis test that Par could use to
compare the driving distances of the
current and new golf balls.
2. Analyze the data to provide the
hypothesis testing conclusion. What is
the p-value for your test? What is your
recommendation for Par, Inc.?
3. Provide descriptive statistical
summaries of the data for each model.
4. What is the 95% confidence interval for
the population mean driving distance of
each model, and what is the 95%
confidence interval for the difference
between the means of the two
populations?
5. Do you see a need for larger sample sizes
and more testing with the golf balls?
Discuss.
Current Proposed
76
74
76
75
77
77
74
78
76
74
74
80
74
73
77
73
72
78
78
76
73
76
78
74
75
77
80
69
79
76
72
75
69
72
79
75
72
72
70
76
70
72
81
77
76
73
78
77
72
69
82
77
72
75
73
76
71
74
70
77
77
75
78
78
73
72
79
77
82
78
65
78
77
76
79
75
73
76
76
76
81
75
69
75
75
77
79
76
78
76
76
73
77
84
74
74
69
79
66
70
74
72
76
80
77
76
75
73
77
77
77
79
75
75
72
82
76
76
74
72
78
71

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