APFIVE A researcher performed a two-sided hypothesis test for a proportion with the hypotheses $$H_0: p = 0.5$$ and $$H_a: p \neq 0.5$$. The resulting p-value was 0.03. Based on this result, the researcher concluded that there is a 97% probability that the alternative hypothesis is true. Which of the following correctly identifies the flaw in this conclusion?
A p-value of 0.03 actually implies a 3% probability that $$p \neq 0.5$$.
There is no mistake; the p-value correctly indicates a 97% chance that $$p \neq 0.5$$.
They should have performed a one-tailed test instead of a two-tailed test.
They misinterpret the p-value; a p-value of 0.03 indicates the probability of observing the data given $$H_0$$ is true, not the probability that $$p \neq 0.5$$.
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