A School Psychologist Interested in the Effect of a Program

question 69

Essay

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.

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Definitions:

Expand

In mathematics, to rewrite an expression or equation in an extended form by distributing or multiplying out brackets.

Pascal's Triangle

A triangular array of numbers in which the edges are 1's, and each interior number is the sum of the two numbers directly above it.

Binomial Coefficient

The number of ways to choose a fixed number of elements out of a larger set, commonly represented as "n choose k."

Expansion

The process of expressing something in an extended form, often used in mathematics to denote the development of an algebraic expression or series.