Question

A study of the effects of exercise used rats bred to have high or low capacity for exercise. The 8 high -capacity rats had mean blood pressure 89 mm Hg and standard deviation 9 mm Hg; the 8 low-capacity rats had mean blood pressure 105 mm Hg with standard deviation 13 mm Hg. We suspect that rats with low capacity for exercise tend to have a higher blood pressure than rats with a high capacity for exercise. To see if this is true, test these with hypotheses for the mean blood pressure of all rats with high capacity (HC) and all rats with low capacity (LC) for exercise:

Answer 1

Let 1 denote the high-capacity rats and 2 denote the low-capacity rats.

The null and alternate hypothesis are:

The test statistic is given by:

Since this is a left-tailed test, so the p-value is given by:

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis
H0 at 5% level of significance.

Thus we can say that rats with low capacity for exercise tend to have a higher blood pressure than rats with a high capacity for exercise.