Question

A researcher is testing whether a majority of the population believes a certain statement is true (H0 : p=0.50 vs HA : p>0.50). After analysis, the researcher runs the hypothesis test and obtains a p-value of 0.3854. Which of the following interpretations of the results is most correct?

a) There is not sufficient evidence to conclude more than half of the population believes the statement is true
b) There is not enough information given to answer this question
c) There is sufficient evidence to conclude more than half of the population believes this statement is true
d) None of these

Answer 1

The correct interpretation of the hypothesis test with a p-value of 0.3854 is that there is not sufficient evidence to conclude that more than half of the population believes the statement is true because the p-value is greater than the standard alpha level of 0.05.

Step-by-step explanation:

A researcher is testing the hypothesis of whether a majority of the population believes a certain statement is true. The null hypothesis (H0) states that the proportion p of the population that believes the statement is true is 0.50, and the alternative hypothesis (HA) states that p > 0.50. After conducting a hypothesis test, the researcher finds a p-value of 0.3854.

When comparing the p-value to the significance level alpha (α), one typically uses a standard α = 0.05. Since the obtained p-value is greater than the significance level (α < p-value), the correct decision is to not reject the null hypothesis. Therefore, there is not sufficient evidence to conclude that more than half of the population believes the statement is true.

This is consistent with option a) which states that there is not sufficient evidence to conclude more than half of the population believes the statement is true. This aligns with the typical interpretation of hypothesis testing results, where failing to reject the null hypothesis suggests that the data do not provide strong evidence against it.