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In: Statistics and Probability

The body mass index​ (BMI) for a sample of men and a sample of women are...

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

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Expert Solution

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

orchestra answered 1 year ago
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