Question

Jacqueline is making the claim that the average time to recovery after a sport injury is greater than 61 days. Therefore, this is a right-tailed test because of "greater than". Since this is a right-tailed test, α and p-value will be areas on the right side of the distribution. In making the decision to reject or not reject H0, recall the criterion for comparing the p-value to α. If p≤α, reject H0 . Since the p-value 0.2296 is greater than the significance level a=0.01, do not reject the null hypothesis. Content attributon

Answer 1

Hypothesis testing involves comparing the p-value to the significance level (alpha) to make a decision on the null hypothesis (H0). If the p-value is less than alpha, H0 is rejected; if greater, H0 is not rejected.

Step-by-step explanation:

The question relates to hypothesis testing in statistics, specifically to how we make decisions about the null hypothesis (H0) based on the p-value and the significance level (alpha). In hypothesis testing, we compare the p-value to alpha to decide whether to reject or not reject H0.

When the p-value is less than alpha (α), which is the significance level, we reject the null hypothesis as there is sufficient evidence against it. Conversely, if the p-value is greater than alpha, we do not reject the null hypothesis because we don't have enough evidence to do so, indicating that the sample data are consistent with H0.

To illustrate, if alpha is set to 0.05 and the calculated p-value is 0.0396, since the p-value is lower (α > p-value), we would reject H0. On the other hand, if the p-value were 0.2296, as mentioned in the initial example, it's greater than alpha of 0.01; thus, we do not reject H0.