A School Psychologist Interested in the Effect of a Program

A school psychologist interested in the effect of a program designed to reduce adjustment problems in newly transferred students knew from her years of working at the school that the average score on a scale of adjustment difficulties for transfer students was 58 with a standard deviation of 10.After starting the program,the psychologist tested 50 students and found their mean to be 52.Using the .01 level of significance,was this difference significant?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Advanced topic: Figure the confidence limits for the 99% confidence interval.
d.Explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but is unfamiliar with hypothesis testing involving a sample of more than one individual.Be sure your explanation includes a discussion of the distribution of mean-what it is,the logic of how it is figured-and its role in the overall hypothesis testing process.Advanced topic: Explain the logic and computation of the confidence intervals.