Question

A randomized comparative experiment examined the effect of the attractiveness of an instructor on the performance of students on a quiz given by the instructor. The researchers found a statistically significant difference in quiz scores between students in a class with an instructor rated as attractive and students in a class with an instructor rated as unattractive (P = 0.005).? When asked to explain the meaning of "p = 0.005," a student says, "This means there is only probability of 0.005 that the null hypothesis is true." Explain what P = 0.005 really means in a way that makes it clear that the student's explanation is wrong.

Answer 1

A p-value of 0.005 means there's a 0.5% chance of getting the observed results if the null hypothesis is correct, suggesting strong evidence against the null hypothesis rather than a probability that the null hypothesis is true.

Step-by-step explanation:

The student's explanation of the p-value is incorrect. A p-value of 0.005 does not represent the probability that the null hypothesis is true. Instead, it indicates how unlikely the observed data would be if the null hypothesis were true. A p-value of 0.005 means that there is only a 0.5% chance of obtaining the observed results, or results more extreme, assuming that the null hypothesis is correct. In practice, when the p-value is less than the significance level (usually 0.05 or 5%), it suggests that there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. Therefore, in the context of the experiment examining the effect of the attractiveness of an instructor on students' quiz performance, the low p-value provides significant evidence against the null hypothesis that there is no difference in quiz scores between the two groups of students.