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The True Meaning of $p$

APSTAT-EV0W2L

A one-sided significance test for a population mean was conducted and the resulting $p$-value was $p = 0.03$.

What is the best interpretation of this $p$-value?

A

There is a $3\%$ chance that the statistic obtained from our sample is equal to the true population mean.

B

We are only $3\%$ confident that our results are correct.

C

Our results are statistically significant at the $\alpha=0.05$ level. We have sufficient evidence to reject the null hypothesis.

D

The probability that we will make a type $II$ error based on our results is about $3\%$.

E

If our null hypothesis is true, the probability is only $3\%$ that we would obtain a sample statistic as far away from the hypothesized mean as the statistic we actually got from our sample.