As part of a study on pulse rates, a random sample of 10 study participants had their pulse rate taken and asked to sit quietly for 5 minutes. At the end of 5 minutes, their pulse rates were taken again. The mean difference between the two pulse rates for the 10 participants is -1.2 beats per minute with standard deviation of 2.97. Researchers are interested in testing whether or not the mean difference in pulse rates before and after the 5 minute waiting period is 0.

Based on the t-test statistic and p-value, researchers decide to fail to reject the null hypothesis. Select the correct conclusion for this hypothesis test. a. There is enough evidence to conclude the mean difference in pulse rates before and after the 5 minute waiting period is 0.b. There is enough evidence to conclude the mean difference in pulse rates before and after the 5 minute waiting period is different from 0.c. There is not enough evidence to conclude the mean difference in pulse rates before and after the 5 minute waiting period is 0.d. There is not enough evidence to conclude the mean difference in pulse rates before and after the 5 minute waiting period is different from 0.

The right option is:

b. There is enough evidence to conclude the mean difference in pulse rates before and after the 5 minute waiting period is different from 0.

Step-by-step explanation:

The null hypothesis is the opposite to the claim that the researchers are trying to prove. In this case, it will state that there is no difference in the mean pulse rates or, in other words, that the mean difference in pulse rates before and after the 5 minute waiting period is 0 (μ=0).

The claim of the researchers, that will be expressed in the alternative hypothesis, is that the mean difference in pulse rates before and after the 5 minute waiting period differs from 0 (μ≠0).

If the null hypothesis is rejected, is because the test shows that there is enough evidence to support the claim that the mean difference in pulse rates before and after the 5 minute waiting period differs from 0 (true alternative hypothesis).

Note: If the null hypothesis wasn't rejected, the conclusion would have been that there is no evidence o support the claim that the mean difference in pulse rates before and after the 5 minute waiting period differs from 0.

The right option is:

b. There is enough evidence to conclude the mean difference in pulse rates before and after the 5 minute waiting period is different from 0.

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