BEHAVIORAL SCIENCES STAT-PKG
2nd Edition
ISBN: 9781337205221
Author: Heiman
Publisher: CENGAGE L
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Chapter 1, Problem 12SP
(a) What are
(b) What are
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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/ }
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(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(·).
math
Chapter 1 Solutions
BEHAVIORAL SCIENCES STAT-PKG
Ch. 1 - What is the goal of behavioral research?Ch. 1 - Why is it important for students of behavioral...Ch. 1 - (a) What is a population? (b) What is a sample?...Ch. 1 - (a) What is a variable? (b) What is a quantitative...Ch. 1 - What pattern among the X and Y scores do you see...Ch. 1 - What is the difference in the pattern among the X...Ch. 1 - Prob. 7SPCh. 1 - Prob. 8SPCh. 1 - Prob. 9SPCh. 1 - In an experiment, what is the dependent variable?
Ch. 1 - What is the difference between the independent...Ch. 1 - (a) What are descriptive statistics used for?...Ch. 1 - Prob. 13SPCh. 1 - Prob. 14SPCh. 1 - Prob. 15SPCh. 1 - What are the two aspects of a study to consider...Ch. 1 - Researcher A gives participants various amounts of...Ch. 1 - Maria asked a sample of college students about...Ch. 1 - In the following experiments, identify the...Ch. 1 - Use the words relationship, sample, population,...Ch. 1 - Which sample in problem 21 shows the most...Ch. 1 - What pattern do we see when the results of an...Ch. 1 - Indicate whether a researcher would conduct an...Ch. 1 - In the chart below, identify the characteristics...
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