Question

Example 14.1 (page 360) described NHANES survey data on the body mass index (BMI) of 654 young women. The mean BMI in the sample was x¯¯¯x¯ = 26.8. We treated these data as an SRS from a Normally distributed population with standard deviation σσ = 7.5.

(a) Give three confidence intervals for the mean BMI μμ in this population, using 90%, 95%, and 99% confidence.
(b) What are the margins of error for 90%, 95%, and 99% confidence? 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?

(1) 90%: to
      95%: to
      99%: to
(2) 90%:

Emissions of sulfur dioxide by industry sett off chemical changes in the atmosphere that result in "acid rain". The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a Canadian forest follow a Normal distribution with standard deviation σσ = 0.5. A sample of n days finds that the mean pH is x¯¯¯x¯ = 4.8. What are the P- Values for tests of sample sizes n = 5, n = 15 and n = 40?

n = 5:
n = 15:
n = 40:

      95%:
      99%:

Answer 1