Question

1. Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3​ inches, with a standard deviation of 2.9 inches. A baseball analyst wonders whether the standard deviation of heights of​ major-league baseball players is less than 2.9 inches. The heights​ (in inches) of 20 randomly selected players are shown in the table.

72
74
71
72
76
70
77
76
72
72
77
73
75
70
73
74
75
73
74
73

2. Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the​ P-value method or the traditional method of testing hypotheses. Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2​ ft, which was the standard deviation for the old production method. If it appears that the standard deviation is​ greater, does the new production method appear to be better or worse than the old​ method? Should the company take any​ action?

-44
79
-21
-72
-42
15
16
51
-6
-52
-108
-108

3. The data table contains waiting times of customers at a​ bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 2.3 ​minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.01 Complete parts​ (a) through​ (d) below.

customer waiting times in minutes

8.1
7.2
6.4
6.6
6.4
7.1
6.7
6.8
8.5
6.1
8.6
6.6
14.9
7.1
6.9
7.3
7.2
6.8
7.7
8.4
8.7
7.8
6.5
11.9
7.3
6.2
6.3
7.8
7.5
6.1
12.4
6.4
6.9
9.9
4.9
7.7
6.1
7.8
6.4
7.4
14.8
7.5
8.9
7.2
7.1
6.1
7.7
6.6
7.8
6.9
6.4
6.2
6.1
7.2
6.8
7.7
6.6
7.3
8.6
7.7

Answer 1