Chapter 10, Problem 11

Body mass index is calculated by dividing a person's weight by the square of his or her height; it is a measure of the extent to which an individual is overweight. For the population of middle-agedmen who later develop diabetes mellitus, the distribution of baseline body mass indices is approximately normal with an unknown mean and a standard deviation .A sample of 58 men selected from this group has mean x-bar = 25.0 kg/m² and standard deviation s = 2.7 kg/m².

a. Construct a 95% confidence interval for tech population mean .

b. At the 0.05 level of significance, test whether the mean baseline body mass index for the population of middle aged men who develop diabetes is equal to 24.0 kg/m², the mean for the population of men who do not. What is the p-value of the test?

c. What do you conclude?

d. Based on the 95% confidence interval, would you have expected to reject or to not reject the null hypothesis? Why?

Reference:

Percentiles of t distribution link:

http://personal.psu.edu/acq/401/tables/t.pdf

According to my book,

df = 0.10 = 90% (link)

df = 0.05 = 95% (link)

df = 0.025 = 97.5% (link)

df= 0.01 = 99% (link)

df = 0.005 = 99.5% (link)

df = 0.0005 = 99.9% (link)