Question 24
1 pts

A researcher wants to test achievement scores for home schooled $4^{\text {th }}$ graders. He knows that the population average for achievement scores of students who attend school is 250 . He samples 110 home schooled $4^{\text {th }}$ graders and finds and achievement level of 272 with a standard deviation of 10 . Using a 0.01 significance level, the research finds the following:
\[
\begin{array}{l}
\mathrm{H}_{1}: \mu \neq 250 \\
\mathrm{z}_{\alpha}:+/-2.57 \\
\mathrm{z}=2.20
\end{array}
\]

Based on this information, what would you conclude?
Fail to reject the null hypothesis
Reject the null hypothesis

Question 25
$1 \mathrm{pts}$

Step 1 ：The question is asking us to determine whether we should reject or fail to reject the null hypothesis based on the given z-scores. The null hypothesis is that the population mean is equal to 250. The alternative hypothesis is that the population mean is not equal to 250.

Step 2 ：The z-score for the sample is 2.20 and the critical z-score (z_alpha) is +/-2.57.

Step 3 ：If the z-score of the sample is greater than the critical z-score, we reject the null hypothesis. If the z-score of the sample is less than the critical z-score, we fail to reject the null hypothesis.

Step 4 ：In this case, the z-score of the sample (2.20) is less than the critical z-score (2.57). Therefore, we fail to reject the null hypothesis.

Step 5 ：Final Answer: \(\boxed{\text{Fail to reject the null hypothesis}}\)