Discussion:
(1) Freshman 15 Weight gains. Based on the sample results, find the best point estimate of the percentage of college students who gain weight in their freshman year.
| SEX |
WTSEP |
WTAPR |
BMISP |
BMIAP |
| M |
72 |
59 |
22.02 |
18.14 |
| M |
97 |
86 |
19.7 |
17.44 |
| M |
74 |
69 |
24.09 |
22.43 |
| M |
93 |
88 |
26.97 |
25.57 |
| F |
68 |
64 |
21.51 |
20.1 |
| M |
59 |
55 |
18.69 |
17.4 |
| F |
64 |
60 |
24.24 |
22.88 |
| F |
56 |
53 |
21.23 |
20.23 |
| F |
70 |
68 |
30.26 |
29.24 |
| F |
58 |
56 |
21.88 |
21.02 |
| F |
50 |
47 |
17.63 |
16.89 |
| M |
71 |
69 |
24.57 |
23.85 |
| M |
67 |
66 |
20.68 |
20.15 |
| F |
56 |
55 |
20.97 |
20.36 |
| F |
70 |
68 |
27.3 |
26.73 |
| F |
61 |
60 |
23.3 |
22.88 |
| F |
53 |
52 |
19.48 |
19.24 |
| M |
92 |
92 |
24.74 |
24.69 |
| F |
57 |
58 |
20.69 |
20.79 |
| M |
67 |
67 |
20.49 |
20.6 |
| F |
58 |
58 |
21.09 |
21.24 |
| F |
49 |
50 |
18.37 |
18.53 |
| M |
68 |
68 |
22.4 |
22.61 |
| F |
69 |
69 |
28.17 |
28.43 |
| M |
87 |
88 |
23.6 |
23.81 |
| M |
81 |
82 |
26.52 |
26.78 |
| M |
60 |
61 |
18.89 |
19.27 |
| F |
52 |
53 |
19.31 |
19.75 |
| M |
70 |
71 |
20.96 |
21.32 |
| F |
63 |
64 |
21.78 |
22.22 |
| F |
56 |
57 |
19.78 |
20.23 |
| M |
68 |
69 |
22.4 |
22.82 |
| M |
68 |
69 |
22.76 |
23.19 |
| F |
54 |
56 |
20.15 |
20.69 |
| M |
80 |
82 |
22.14 |
22.57 |
| M |
64 |
66 |
20.27 |
20.76 |
| F |
57 |
59 |
22.15 |
22.93 |
| F |
63 |
65 |
23.87 |
24.67 |
| F |
54 |
56 |
18.61 |
19.34 |
| F |
56 |
58 |
21.73 |
22.58 |
| M |
54 |
56 |
18.93 |
19.72 |
| M |
73 |
75 |
25.88 |
26.72 |
| M |
77 |
79 |
28.59 |
29.53 |
| F |
63 |
66 |
21.89 |
22.79 |
| F |
51 |
54 |
18.31 |
19.28 |
| F |
59 |
62 |
19.64 |
20.63 |
| F |
65 |
68 |
23.02 |
24.1 |
| F |
53 |
56 |
20.63 |
21.91 |
| F |
62 |
65 |
22.61 |
23.81 |
| F |
55 |
58 |
22.03 |
23.42 |
| M |
74 |
77 |
20.31 |
21.34 |
| M |
74 |
78 |
20.31 |
21.36 |
| M |
64 |
68 |
19.59 |
20.77 |
| M |
64 |
68 |
21.05 |
22.31 |
| F |
57 |
61 |
23.47 |
25.11 |
| F |
64 |
68 |
22.84 |
24.29 |
| F |
60 |
64 |
19.5 |
20.9 |
| M |
64 |
68 |
18.51 |
19.83 |
| M |
66 |
71 |
21.4 |
22.97 |
| F |
52 |
57 |
17.72 |
19.42 |
| M |
71 |
77 |
22.26 |
23.87 |
| F |
55 |
60 |
21.64 |
23.81 |
| M |
65 |
71 |
22.51 |
24.45 |
| M |
75 |
82 |
23.69 |
25.8 |
| F |
42 |
49 |
15.08 |
17.74 |
| M |
74 |
82 |
22.64 |
25.33 |
| M |
94 |
105 |
36.57 |
40.86 |
a. Construct a 95% confidence interval estimate of the percentage of college students who gain weight in their freshman year.
b. Assuming that you are a newspaper reporter, write a statement that describes the results. Include all of the relevant information.
(2) NCAA Football coach salaries. A simple random sample of 40 salaries of NCAA football coaches has a mean of $415,953. Assume that o- = $463,364.
a. Find the best point estimate of the mean salary of all NCAA football coaches.
b. Construct a 95% confidence interval estimate of the mean salary of an NCAA football coach.
c. Does the confidence interval contain the actual population mean of $474,477?
(3) Acupuncture for Migraines. In a study designed to test the effectiveness of acupuncture for treating migraines, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for the acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The number of migraine attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2.
a. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture.
b. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those given a sham treatment.
c. Compare the two confidence intervals. What do the results suggest about the effectiveness of acupuncture?
(4) Weights of M&Ms lists 100 weights (in grams) of M&M candies. The minimum weight is 0.696 g and the maximum weight is 1.015 g.
| Red |
Orange |
Yellow |
Brown |
Blue |
Green |
| 0.751 |
0.735 |
0.883 |
0.696 |
0.881 |
0.925 |
| 0.841 |
0.895 |
0.769 |
0.876 |
0.863 |
0.914 |
| 0.856 |
0.865 |
0.859 |
0.855 |
0.775 |
0.881 |
| 0.799 |
0.864 |
0.784 |
0.806 |
0.854 |
0.865 |
| 0.966 |
0.852 |
0.824 |
0.840 |
0.810 |
0.865 |
| 0.859 |
0.866 |
0.858 |
0.868 |
0.858 |
1.015 |
| 0.857 |
0.859 |
0.848 |
0.859 |
0.818 |
0.876 |
| 0.942 |
0.838 |
0.851 |
0.982 |
0.868 |
0.809 |
| 0.873 |
0.863 |
|
|
0.803 |
0.865 |
| 0.809 |
0.888 |
|
|
0.932 |
0.848 |
| 0.890 |
0.925 |
|
|
0.842 |
0.940 |
| 0.878 |
0.793 |
|
|
0.832 |
0.833 |
| 0.905 |
0.977 |
|
|
0.807 |
0.845 |
|
0.850 |
|
|
0.841 |
0.852 |
|
0.830 |
|
|
0.932 |
0.778 |
|
0.856 |
|
|
0.833 |
0.814 |
|
0.842 |
|
|
0.881 |
0.791 |
|
0.778 |
|
|
0.818 |
0.810 |
|
0.786 |
|
|
0.864 |
0.881 |
|
0.853 |
|
|
0.825 |
|
|
0.864 |
|
|
0.855 |
|
|
0.873 |
|
|
0.942 |
|
|
0.880 |
|
|
0.825 |
|
|
0.882 |
|
|
0.869 |
|
|
0.931 |
|
|
0.912 |
|
|
|
|
|
0.887 |
|
|
|
|
|
0.886 |
|
a. Use the range rule of thumb to estimate o, the standard deviation of weights of all such M&Ms.
b. The 100 weights have a standard deviation of 0.0518 g. Construct a 95% confidence interval estimate of the standard deviation of weights of all M&MS.
c. Does the confidence interval from part b contain the estimated value of o- from part a? What do the results suggest about the estimate from part a?