In: Statistics and Probability
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 30.930.9 22.322.3 29.929.9 30.930.9 27.227.2 31.731.7 26.526.5 20.220.2 26.626.6 30.530.5 Women nbspWomen 18.218.2 20.720.7 22.222.2 28.428.4 17.117.1 20.320.3 23.923.9 31.831.8 20.820.8 20.720.7 LOADING... Click the icon to view the table of Chi-Square critical values. a. Construct aa 9090% confidence interval estimate of the standard deviation of BMIs for men. nothingless than
We have asked to construct a 90% confidence interval for the population standard deviation of BMI for men.
The random sample of men is given and using that data we find the sample standard deviation of BMI for men, and then using that we'll construct the 90% confidence interval for the population standard deviation of BMI for men.
BMI for men |
||
30.9 | 3.23 | 10.4329 |
22.3 | -5.37 | 28.8369 |
29.9 | 2.23 | 4.9729 |
30.9 | 3.23 | 10.4329 |
27.2 | -0.47 | 0.2209 |
31.7 | 4.03 | 16.2409 |
26.5 | -1.17 | 1.3689 |
20.2 | -7.47 | 55.8009 |
26.6 | -1.07 | 1.1449 |
30.5 | 2.83 | 8.0089 |
sample standard deviation of mens BMI is-
Formula to calculate the confidence interval for standard deviation is-
Critical value:
So, the 90% confidence interval for the population standard deviation for mens BMI is calculated as (2.8504, 6.4296) Or