Question: A school counselor was interested in the effect of a new program designed to reduce adjustment problems in newly transferred students. From her years of working at the school, she knew that the average score on a scale of adjustment difficulties for a transfer student was 58, with a standard deviation of 10. After the new program had been implemented, she tested 50 students and found their mean to be 52.

1. Would you use a one-tailed or two-tailed test for this research question? (Be careful; subsequent questions depend upon you figuring this out.)
2. Estimate the variance and the standard deviation of the distribution of means for this problem
3. Was this difference significant at the .01 level? Follow the steps of hypothesis testing completely when outlining your answer.
4. Sketch the distributions involved (population normal curve, distribution of means, and sample, as in examples in your textbook). (2.5 points)
5. Figure the confidence limits for the 99% confidence interval for this problem (5 points)
6. Why is the distribution of means narrower than the normal curve? (2.5 points)
7. What is the effect of increasing the number of samples on the distribution of means?

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