Final answer:
We will reject the null hypothesis at a significance level of 0.05 if the p-value is less than 0.05, which in the given options is only true for option b (0.025). The null hypothesis for a claim that students spend exactly 3 hours studying would be H0: μ = 3.
Step-by-step explanation:
To determine which of the following values will lead us to reject the null hypothesis at a level of significance of 0.05, we compare each value to the significance level. Since the only value that is lower than 0.05 is option b (0.025), this is the value that will lead us to reject the null hypothesis.
In hypothesis testing, if the p-value is lower than the alpha level (in this case, 0.05), we have enough evidence to reject the null hypothesis and accept the alternative hypothesis.
When a professor of statistics wishes to refute the claim that the average student spends 3 hours studying for a midterm exam, the null hypothesis (H0) would be that the average is indeed 3 hours (H0: μ = 3), and the alternative hypothesis (Ha) would be the negation of that claim, which could be that the average is not 3 hours (Ha: μ ≠ 3) if we are doing a two-tailed test, or that the average is less than 3 hours (Ha: μ < 3) if the claim or study is specifically directed toward proving the average is less.