Question

A journalist makes the following claim: “More than 75% of recent college graduates believe they are ready for a professional work environment.” Later, a researcher collects data and performs a hypothesis test for this claim. The researcher concludes, “With a significance level of 0.05, there is enough evidence from this sample to support the journalist’s claim.”

Only one of the following statements is true. Select the statement that is true.

		“It is possible that a Type II error occurred. The researcher should have failed to support the journalist’s claim, and failing to support a claim that is true is a Type II error.”
		“It is possible that a Type I error occurred. Since the researcher supported the journalist’s claim, it’s possible that the researcher made a calculational mistake in the hypothesis test, and then the researcher’s conclusion would be an error.”
		“It is possible that a Type II error occurred. The researcher should have failed to reject the journalist’s claim, and failing to reject a claim that is false is a Type II error.”
		“It is possible that a Type I error occurred. Since the researcher supported the journalist’s claim, it’s possible the claim is incorrect and then the researcher’s conclusion would be an error.”

Answer 1

Here claim is that p>0.75

So hypothesis is vs

Here researcher supports the claim, which means he rejects the null hypothesis

Now Type I error is rejecting the true null hypothesis

Type II error is failing to reject the false null hypothesis

Now here researcher might have made Type I error as he rejected null hypothesis and it might be incorrect

So answer here is

“It is possible that a Type I error occurred. Since the researcher supported the journalist’s claim, it’s possible the claim is incorrect and then the researcher’s conclusion would be an error.”