You conduct a simulation regarding which team spectators at a football game support. Your null hypothesis is that there are equal proportions of people supporting the home team and the visiting team. Your alternative hypothesis is that there is a higher proportion of people supporting the home team.

You determine that the results of your simulation have a p-value of 0.002. What does this mean?

A) Under the tested hypothesis, the outcome of the simulation has a probability of 2%. With a significance level of 1%, you should reject the null hypothesis.
B) Under the tested hypothesis, the outcome of the simulation has a probability of 2%. With a significance level of 1%, you should fail to reject the null hypothesis.
C) Under the tested hypothesis, the outcome of the simulation has a probability of 0.2%. With a significance level of 1%, you should reject the null hypothesis.
D) Under the tested hypothesis, the outcome of the simulation has a probability of 0.2%. With a significance level of 1%, you should fail to reject the null hypothesis.

1 answer

The p-value of 0.002 indicates that, under the null hypothesis (which states that there are equal proportions of supporters for the home and visiting teams), the observed results (or results at least as extreme) would occur with a probability of 0.2%.

Given this p-value, if you set a significance level of 1% (0.01), the p-value is less than the significance level (0.002 < 0.01), which means you have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis (which posits that there is a higher proportion of people supporting the home team).

Therefore, the correct interpretation is:

A) Under the tested hypothesis, the outcome of the simulation has a probability of 2%. With a significance level of 1%, you should reject the null hypothesis.

(Note: there’s a small discrepancy in the wording regarding 0.2% vs. 2%, but A captures the essence of rejecting the null hypothesis based on the p-value being less than the significance level.)