question archive The body mass index (BMI) for a sample of men and a sample of women are given below
The body mass index (BMI) for a sample of men and a sample of women are given below
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The body mass index (BMI) for a sample of men and a sample of women are given below. Assume the samples are simple random samples obtained from populations with normal distributions.
| Men | 23.6 | 32.5 | 21.2 | 25.5 | 25.6 | 32.3 | 32.4 | 30.3 | 26.1 | 21.5 | |
| Women | 18.8 | 20.7 | 24.9 | 30.7 | 18.5 | 23.6 | 18.5 | 30.7 | 17.4 |
24.3 |
A. Construct a 95% confidence interval estimate of the standard deviation of BMIs for men. ? < σ men < ?
B. Construct a 95% confidence interval estimate of the standard deviation of BMIs for women. ? < σ women < ?
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Answer:
|
Confidence Interval Estimate for the Mean for men |
|
|
Data |
|
|
Sample Standard Deviation |
4.45670531 |
|
Sample Mean |
27.1 |
|
Sample Size |
10 |
|
Confidence Level |
95% |
|
Intermediate Calculations |
|
|
Standard Error of the Mean |
1.409333964 |
|
Degrees of Freedom |
9 |
|
t Value |
2.2622 |
|
Interval Half Width |
3.1881 |
|
|
|
|
Confidence Interval |
|
|
Interval Lower Limit |
23.91 |
|
Interval Upper Limit |
30.29 |
|
Confidence Interval Estimate for the Mean for women |
|
|
Data |
|
|
Sample Standard Deviation |
4.322904116 |
|
Sample Mean |
21.93333333 |
|
Sample Size |
9 |
|
Confidence Level |
95% |
|
Intermediate Calculations |
|
|
Standard Error of the Mean |
1.440968039 |
|
Degrees of Freedom |
8 |
|
t Value |
2.3060 |
|
Interval Half Width |
3.3229 |
|
|
|
|
Confidence Interval |
|
|
Interval Lower Limit |
18.61 |
|
Interval Upper Limit |
25.26 |
