Question

An NHANES report gives data for 647 women aged 20–29 years. The BMI of these 647 women was ?¯= 25.8 . On the basis of this sample, we want to estimate the BMI ? in the population of all 20.6 million women in this age group. We treated these data as an SRS from a Normally distributed population with standard deviation ?=7.1 .

(a) Give three confidence intervals for the mean BMI ? in this population, using 90%,95%,and 99% confidence. Enter the lower and upper bound for the 90% confidence interval. (Enter your answers rounded to two decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

lower bound =

upper bound =

Enter the lower and upper bound for the 95% confidence interval. (Enter your answers rounded to two decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

lower bound =

upper bound =

Enter the lower and upper bound for the 99% confidence interval. (Enter your answers rounded to two decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

lower bound =

upper bound =

(b) What are the margin of errors for 90%,95%,and 99% confidence? (Enter your answers rounded to two decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

margin of error for a 90% confidence interval =

margin of error for a 95% confidence interval =

margin of error for a 99% confidence interval =

Select the explanation that correctly describes how increasing the confidence level changes the margin of error of a confidence interval when the sample size and population standard deviation remain the same.

The margin of error increases as the confidence level increases.

The margin of error decreases as the confidence level increases.

The margin of error remains the same as the confidence level increases.

The margin of error is unaffected by the confidence level.

Answer 1

(a)

25.34	confidence interval 90.% lower
26.26	confidence interval 90.% upper

25.25	confidence interval 95.% lower
26.35	confidence interval 95.% upper

25.08	confidence interval 99.% lower
26.52	confidence interval 99.% upper

(b)

0.46	margin of error

0.55	margin of error

0.72	margin of error

The margin of error increases as the confidence level increases.

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