Question

Suppose we conduct a hypothesis test to determine if an exercise program helps people lose weight. We measure the weight of a random sample of participants before and after they complete the exercise program. The mean number of pounds lost for the sample turns out to be 7.9 lbs. The hypotheses for the test are: H0: The program is not effective for weight loss. Ha: The program is effective for weight loss. The P-value for the test turns out to be 0.012. Which of the following is the appropriate conclusion, assuming that all conditions for inference are met and the level of significance is 0.05? (i) We reject H0---this sample does not provide significant evidence that the program is effective. (ii) We reject H0---this sample provides significant evidence that the program is effective. (iii) We fail to reject H0---this sample provides significant evidence that the program is not effective. (iv) We fail to reject H0---this sample does not provide significant evidence that the program is effective.

Answer 1

Answer: (ii) We reject H0---this sample provides significant evidence that the program is effective.

Explanation:

The null hypothesis is

The program is not effective for weight loss.

The alternative hypothesis is

The program is effective for weight loss.

If the P-value for the test turns out to be 0.012, and the level of significance is 0.05, then

Alpha, 0.05 > p value, 0.012

Therefore, there is enough evidence to reject the null hypothesis. We then accept the alternative hypothesis.

The correct option is

(ii) We reject H0---this sample provides significant evidence that the program is effective.