Question

A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%. To test this claim, a survey asked 500 randomly selected college students if they planned to perform community service after graduation. Of those students, 195 indicated they planned to perform community service.The following is the setup m the following hypothesis test:H0:p=0.35Ha:p>0.35In this example, the p-value was determined to be 0.030.Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) .Select the correct answer below:A: The decision is to reject the Null Hypothesis.The conclusion is that there is enough evidence to support the claim.B: The decision is to fail to reject the Null Hypothesis.The conclusion is that there is not enough evidence to support the claim.

Answer 1

A) The decision is to reject the null hypothesis. The conclusion is that there is enough evidence to support the claim.

Explanation:

In this case, the sample proportion was 0.39 and the P-value 0.03. The significance level is 0.05. For us to take a decision, we need to compare the P-value with the significance level.

Since the P-value is less than the significance level, we reject the null hypotesis and conclude that there is enough evidence to support the claim.

In this case, a P-value of 0.03 means that there is a 3% chance of a sample proportion being 0.39 when the true population proportion is 0.35. Since the chance is so low, we conclude that there is enough evidence to reject the hypothesis that the population proportion is 0.35 and we adopt the alternative hypothesis, which claims that the population proportion is greater than 0.35.