As part of a study investigating the effects of vigorous exercise on risk of coronary heart disease, researchers measured HDL concentrations (mg/dL) in a sample of 19 male marathon runners as well as in a sample of 32 men who do not regularly exercise. The data are summarized below: Mean St. Dev. Marathon runners 51.3 mg/dL 14.2 mg/dL Do not exercise 44.0 mg/dL 15.0 mg/dL.

Assuming that the two distributions of HDL concentrations are normally distributed with equal variances, run the appropriate test to determine if there is a significant difference between marathon runners and men who don’t exercise. Use t51*= ± 2.009 Note: Pooled SE = 2.43 mg/dL (2pts)

There is a significant difference between marathon runners and men who don't exercise.

Step-by-step explanation:

Null hypothesis: There is no significant difference between marathon runners and men who don't exercise.

Alternate hypothesis: There is a significant difference between marathon runners and men who don't exercise.

Sample 1 (marathon runners)

mean = 51.3 mg/dL

sd = 14.2 mg/dL

n = 19

Sample 2 (men who don't exercise)

mean = 44 mg/dL

sd = 15 mg/dL

n = 32

Pooled SE = 2.43 mg/L

Test statistic (t) = (mean 1 - mean 2) ÷ sqrt[pooled SE(1/n1 + 1/n2)] = (51.3 - 44) ÷ sqrt[2.43(1/19 + 1/32) = 7.3 ÷ sqrt(0.204) = 7.3 ÷ 0.452 = 16.2

The test is a two-tailed test. The critical value is given as 2.009. For a two-tailed test, the region of no rejection of the null hypothesis lies between -2.009 and +2.009.

Conclusion:

Reject the null hypothesis because the test statistic 16.2 falls outside the region bounded by -2.009 and 2.009.

Therefore, there is a significant difference between marathon runners and men who don't exercise.