Question

A component of cholesterol called high-density lipoprotein is known to lower the risk of coronary heart disease. It is believed that runners have increased HDL levels. The following data give details of an HDL study comparing male elite runners with a control group of male nonrunners. At the α=0.05, test the claim that young male elite runners have a higher population mean HDL level than young male nonrunners.

sample	n	x̄	s
elite runners	20	56	12.1
nonrunners	72	49	10.5

Answer 1

First we will check whether the two population of elite runners and nonrunners respectively, have the same variability in HDL level or not.

Test for Equal Variances

95% Bonferroni confidence intervals for standard deviations

Sample N Lower StDev Upper
1 20 2.54845 3.47851 5.38924
2 72 2.72569 3.24037 3.98237

F-Test (normal distribution)
Test statistic = 1.15, p-value = 0.644.

p-value>0.05.Hence we do not have enough evidence to reject the assumption of homogeneity.Now we are goung to do right tailed test for mean HDL level under the homogeneity assumption with Student's t-test.

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 20 56.0 12.1 2.7
2 72 49.0 10.5 1.2

Difference = mu (1) - mu (2)
Estimate for difference: 7.00000
95% lower bound for difference: 2.43900
T-Test of difference = 0 (vs >): T-Value = 2.55 P-Value = 0.006 DF = 90
Both use Pooled StDev = 10.8574

p-value<<.05.Hence we can strongly conclude that the mean HDL level is higher for elite runners than non-runners at 5% signifiacnce level.