Research Methods for the Behavioral Sciences
Research Methods for the Behavioral Sciences
5th Edition
ISBN: 9780357231913
Author: Frederick J Gravetter; Lori-Ann B. Forzano
Publisher: Cengage Limited
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Chapter 10, Problem 5E

In this chapter, we described a study in which Skjoeveland (2001) examined the effect of street parks on social interactions (p. 288). Although the results clearly showed greater social interaction in neighborhoods in which parks were built, the study does not justify a conclusion that building parks causes an increase in social interaction. Explain why the conclusion is not justified.

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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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