Question

State whether you agree or disagree with the following statement, and explain why or why not:

Since the performance variables (bavg, hrunsyr, and rbisyr) all have p-values > .10, we should conclude that performance does not have a statistically significant effect on salary once we control for experience (years) and amount played (gamesyr).

Answer 1

The p-values for the performance variables are greater than .10, indicating there is insufficient evidence to conclude that performance has a statistically significant effect on salary once we control for experience and amount played.

Step-by-step explanation:

The statement suggests that since the performance variables (bavg, hrunsyr, and rbisyr) all have p-values > .10, we should conclude that performance does not have a statistically significant effect on salary once we control for experience (years) and amount played (gamesyr).

To determine whether this conclusion is valid, we need to understand the concept of statistical significance and how it relates to hypothesis testing. In hypothesis testing, we compare the p-value to a predetermined significance level (alpha) to make a decision. If the p-value is greater than alpha, we fail to reject the null hypothesis. If the p-value is less than or equal to alpha, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

In this case, since the p-values for the performance variables are all greater than .10, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest that performance has a statistically significant effect on salary once we control for experience and amount played. However, it's important to note that failing to reject the null hypothesis does not prove that the null hypothesis is true. It simply means that we do not have enough evidence to support the alternative hypothesis.

Answer 2

I disagree with the statement; a p-value greater than the alpha level of 0.05 typically indicates insufficient evidence to reject the null hypothesis, suggesting performance variables may not significantly affect salary after controlling for experience and games played per year.

Step-by-step explanation:

I disagree with the statement that performance does not have a statistically significant effect on salary once we control for experience (years) and amount played (gamesyr) because the performance variables (bavg, hrunsyr, and rbisyr) all have p-values > .10. This conclusion is based on the common statistical practice where a p-value greater than the chosen alpha level (commonly set at 0.05) suggests that there is not enough evidence to reject the null hypothesis.

In hypothesis testing, the p-value is used to determine the strength of the results in supporting the hypothesis. If the p-value is low (typically under 0.05), it suggests that the data is unlikely to occur under the null hypothesis, and thus we have enough evidence to reject the null hypothesis. Conversely, a high p-value indicates that the data is likely to occur under the null hypothesis, leading to the conclusion that there is insufficient evidence to reject it.

Given that the p-values for the performance variables are greater than 0.10, this suggests that the evidence does not meet the usual threshold of statistical significance (assuming the commonly used alpha of 0.05) to indicate that the performance variables significantly affect the salary after accounting for experience and games played per year. Therefore, at a 5 percent significance level, there is insufficient evidence to conclude that these performance metrics significantly impact the salary.