You are using a sample of size 200 to conduct a hypothesis test in which you want to determine whether a certain population proportion $\pi$ has decreased since last year.If the null hypothesis is $\pi$ .5 and the test statistic turns out to be -1.74, you should conclude, at the .05 significance level, that the population proportion has, in fact, decreased.

Question

You are using a sample of size 200 to conduct a hypothesis test in which you want to determine whether a certain population proportion  $\pi$ has decreased since last year.If the null hypothesis is  $\pi$ > .5 and the test statistic turns out to be -1.74, you should conclude, at the .05 significance level, that the population proportion has, in fact, decreased.

Quizplus · Accepted Answer

Given the null hypothesis is about the proportion being greater than 0.5 and the test statistic is negative (-1.74), this indicates that the sample proportion is less than the hypothesized population proportion. At the .05 significance level, a test statistic of -1.74 typically falls within the critical region for a one-tailed test (depending on the exact distribution being used, but commonly true for z-tests), leading to the rejection of the null hypothesis. Therefore, you would conclude that the population proportion has decreased.

You Are Using a Sample of Size 200 to Conduct π\piπ

You Are Using a Sample of Size 200 to Conduct $\pi$