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 $1 \mathrm{pts}$
Solution
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: \(\boxed{\text{Fail to reject the null hypothesis}}\)
