Essentials of Statistics for the Behavioral Sciences
Essentials of Statistics for the Behavioral Sciences
8th Edition
ISBN: 9781133956570
Author: Frederick J Gravetter, Larry B. Wallnau
Publisher: Cengage Learning
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Chapter 13, Problem 23P

Example 13.1 in this chapter described a two-factor study examining performance under two audience conditions (factor B) for high and low self-esteem participants (factor A). The following summary table presents possible results from the analysis of that study. Assuming that the study used a separate sample of n = 15 participants in each treatment condition (each cell), fill in the missing values in the table. (Hint: Start with the df values.)

Source SS df MS  
Between treatments 67 _____    
Audience ____ _____ _____ F =______
Self-esteem 29 _____ _____ F =
Interaction _____ ______ _____ F = 5.50
Within treatments _____ _____ 4  
Total _____ ______    
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iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).
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Essentials of Statistics for the Behavioral Sciences

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