How do you interpret a p-value of 0.03 in a test with alpha = 0.05?

How do you interpret a p-value of 0.03 in a test with alpha = 0.05?

• A. Do not reject H0; insufficient evidence
• B. Reject H0; evidence against H0 at 5%
• C. P-value indicates results are practically significant
• D. The test is inconclusive

Answer: (B)

The main idea here is how p-values relate to a pre-set significance level. The p-value is the probability, under the assumption that the null hypothesis is true, of observing data as extreme or more extreme than what was actually observed. The alpha level of 0.05 is your criterion for calling something statistically significant. Since the observed p-value is 0.03, which is smaller than 0.05, the result meets the significance criterion. This means you reject the null hypothesis and conclude there is evidence against it at the 5% level. Keep in mind that this speaks to statistical significance, not practical significance or effect size. It also does not say the null hypothesis is true or false with certainty, nor does it give the probability that the null is true. If the p-value had been larger than 0.05, you would not reject the null at that level, indicating insufficient evidence to declare statistical significance.

The main idea here is how p-values relate to a pre-set significance level. The p-value is the probability, under the assumption that the null hypothesis is true, of observing data as extreme or more extreme than what was actually observed. The alpha level of 0.05 is your criterion for calling something statistically significant.

Since the observed p-value is 0.03, which is smaller than 0.05, the result meets the significance criterion. This means you reject the null hypothesis and conclude there is evidence against it at the 5% level.

Keep in mind that this speaks to statistical significance, not practical significance or effect size. It also does not say the null hypothesis is true or false with certainty, nor does it give the probability that the null is true. If the p-value had been larger than 0.05, you would not reject the null at that level, indicating insufficient evidence to declare statistical significance.