A p-value of 0.03 at a significance level of 0.05 indicates what?

The null hypothesis should be accepted.

The results were not studied.

The p-value indicates the probability of observing results at least as extreme as those observed under the null.

P-values reflect how surprising the data would be if the null hypothesis were true. A p-value of 0.03 means that, if there were no real effect, there’s about a 3% chance of obtaining results as extreme as what was observed (or more extreme). The significance level of 0.05 is the cutoff for deciding whether to doubt the null; since 0.03 is below 0.05, the result is considered statistically significant and the null would be rejected. This interpretation matches the statement that the p-value indicates the probability of observing results at least as extreme as those observed under the null. The other options don’t fit: accepting the null isn’t how we conclude from a p-value, the result isn’t simply “not studied,” and significance isn’t automatic regardless of the p-value.

The results are statistically significant regardless of the p-value.

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