Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 10.6, Problem 53E
How would you like to live to be 200 years old? For centuries, humankind has sought the key to the mystery of aging. What causes aging? How can aging be slowed? Studies have focused on biomarkers, physical or biological changes that occur at a predictable time in a person’s life. The theory is that, if ways can be found to delay the occurrence of these biomarkers, human life can be extended. A key biomarker, according to scientists, is forced vital capacity (FVC), the volume of air that a person can expel after taking a deep breath. A study of 5209 men and women aged 30 to 62 showed that FVC declined, on the average, 3.8 deciliters (dl) per decade for men and 3.1 deciliters per decade for women.10 Suppose that you wished to determine whether a physical fitness program for men and women aged 50 to 60 would delay aging: to do so, you measured the FVC for 30 men and 30 women participating in the fitness program at the beginning and end of the 50-to 60-year age interval and recorded the drop in FVC for each person. A summary of the data appears in the accompanying table.
- a Do the data provide sufficient evidence to indicate that the decrease in the mean FVC over the decade for the men on the physical fitness program is less than 3.8 dl? Find the attained significance level for the test.
- b Refer to part (a). If you choose α = .05, do the data support the contention that the mean decrease in FVC is less titan 3.8 dl?
- c Test to determine whether the FVC drop for women on the physical fitness program was less than 3.1 dl for the decade. Find the attained significance level for the test.
- d Refer to part (c). If you choose α = .05, do the data support the contention that the mean decrease in FVC is less than 3.1 dl?
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Microsoft Excel include formulas
Question 1
The data shown in Table 1 are and R values for 24 samples of size n = 5 taken from a process producing
bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals
recorded (i.e., 34.5 should be 0.50345).
Table 1: Bearing Diameter Data
Sample Number
I
R
Sample Number
I R
1
34.5
3
13
35.4
8
2
34.2
4
14
34.0
6
3
31.6
4
15
37.1
5
4
31.5
4
16
34.9
7
5
35.0
5
17
33.5
4
6
34.1
6
18
31.7
3
7
32.6
4
19
34.0
8
8
33.8
3
20
35.1
9
34.8
7
21
33.7
2
10
33.6
8
22
32.8
1
11
31.9
3
23
33.5
3
12
38.6 9
24
34.2
2
(a) Set up and R charts on this process. Does the process seem to be in statistical control? If necessary,
revise the trial control limits. [15 pts]
(b) If specifications on this diameter are 0.5030±0.0010, find the percentage of nonconforming bearings pro-
duced by this process. Assume that diameter is normally distributed. [10 pts]
1
4. (5 pts) Conduct a chi-square contingency test (test of independence) to assess whether
there is an association between the behavior of the elderly person (did not stop to talk,
did stop to talk) and their likelihood of falling. Below, please state your null and
alternative hypotheses, calculate your expected values and write them in the table,
compute the test statistic, test the null by comparing your test statistic to the critical
value in Table A (p. 713-714) of your textbook and/or estimating the P-value, and
provide your conclusions in written form. Make sure to show your work.
Did not stop walking to talk
Stopped walking to talk
Suffered a fall
12
11
Totals
23
Did not suffer a fall | 2
Totals
35
37
14
46
60
T
Chapter 10 Solutions
Mathematical Statistics with Applications
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