We have the survey data on the body mass index (BMI) of 667 young women. The mea

Question

We have the survey data on the body mass index (BMI) of 667 young women. The mean BMI in the sample was x = 26.4. We treated these data as an SRS from a Normally distributed population with standard deviation sigma = 7.3. Give confidence intervals for the mean BMI and the margins of error for 90%, 95%, and 99% confidence. (Round your answers to two decimal places.) How does increasing the confidence level change the margin of error of a confidence interval when the sample size and population standard deviation remain the same? Increasing the confidence level causes the margin of error to increase. Increasing the confidence level doesn't affect the margin of error. Increasing the confidence level causes the margin of error to decrease. You may need to use the appropriate Appendix Table to answer this question.

Explanation / Answer

The statcrunch output for 90%, 95% and 99% confidence interval is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 7.3

90% confidence interval results:

95% confidence interval results:

26.953998

99% confidence interval results:

So,

So we can see that increasing the confidence level cause the margin of error to increase.

Option A is correct.

Mean n Sample Mean Std. Err. L. Limit U. Limit 667 26.4 0.28265713 25.93507 26.86493

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