As part of a study investigating the effects of vigorous exercise on risk of cor

Question

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 of marathon runners is 51.3 mg/dL and the standard deviation is 14.2.

The mean of men who do not exercise is 44.0 mg/dL and the standard deviation is 15.

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. Note: Pooled SE = 2.43 mg/dL

Explanation / Answer

Ans:

pooled std.dev=sqrt(((19-1)*14.2^2+(32-1)*15^2)/(19+32-2))=14.71

pooled std. error=14.71*sqrt((1/19)+(1/32))=4.26

Test statistic:

t=(51.3-44)/4.26=1.714

df=19+32-2=49

p-value(2 tailed)=tdist(1.714,49,2)=0.0928

Assume significance level=0.05

As,p-value>0.05,we fail to reject null hypothesis.

There is not enough evidence to conclude that there is a significant difference between marathon runners and men who don’t exercise.

*(pooled SE stated in problem statement is not correct,calculation for SE are given above in solution)

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