Research Methods for the Behavioral Sciences (MindTap Course List)
6th Edition
ISBN: 9781337613316
Author: Frederick J Gravetter, Lori-Ann B. Forzano
Publisher: Cengage Learning
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Chapter 10, Problem 3E
Why are studies that examine the effects of aging not considered true experiments?
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Proposition 1.1 Suppose that X1, X2,... are random variables. The following
quantities are random variables:
(a) max{X1, X2) and min(X1, X2);
(b) sup, Xn and inf, Xn;
(c) lim sup∞ X
and lim inf∞ Xn-
(d) If Xn(w) converges for (almost) every w as n→ ∞, then lim-
random variable.
→ Xn is a
Exercise 4.2 Prove that, if A and B are independent, then so are A and B, Ac and
B, and A and B.
8. Show that, if {Xn, n ≥ 1) are independent random variables, then
sup X A) < ∞ for some A.
Chapter 10 Solutions
Research Methods for the Behavioral Sciences (MindTap Course List)
Ch. 10.1 - Define, compare, and contrast the experimental,...Ch. 10.2 - Define a nonequivalent group design and identify...Ch. 10.2 - Explain how individual differences threaten the...Ch. 10.2 - Describe the two nonexperimental nonequivalent...Ch. 10.2 - Explain how a simple modification of the...Ch. 10.3 - Define a pre-post design and identify examples of...Ch. 10.3 - Identify the threats to internal validity for...Ch. 10.3 - Describe the nonexpenmental pretest-posttest...Ch. 10.3 - Explain how replacing the single observation...Ch. 10.4 - Define cross-sectional and longitudinal designs,...
Ch. 10.5 - Identify the statistical techniques that are...Ch. 10.5 - Explain how the terms quasi-independent variable...Ch. 10 - In addition to the key words, you should also be...Ch. 10 - Explain the distinction between experimental and...Ch. 10 - Why are studies that examine the effects of aging...Ch. 10 - Explain why we can be more confident about causal...Ch. 10 - Give an example of a situation (aside from gender)...Ch. 10 - Mueller and Oppenheimer (2014) conducted a series...Ch. 10 - A researcher measures personality characteristics...Ch. 10 - A researcher wants to describe the effectiveness...Ch. 10 - Explain how the pretest helps minimize the threat...Ch. 10 - Describe the basic characteristics of a pre-post...Ch. 10 - To evaluate the effectiveness of a new television...Ch. 10 - What characteristic differentiates a pretest-post...Ch. 10 - Explain how a time-series design minimizes most...Ch. 10 - A researcher wants to describe how fine motor...Ch. 10 - Although the cohort effect can be a serious...Ch. 10 - Identify the appropriate statistical test for each...Ch. 10 - The college offers all students an optional...
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- 8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.arrow_forward7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).arrow_forward19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.arrow_forward18. Define a bivariate random variable. Provide an example.arrow_forward6. (a) Let (, F, P) be a probability space. Explain when a subset of ?? is measurable and why. (b) Define a probability measure. (c) Using the probability axioms, show that if AC B, then P(A) < P(B). (d) Show that P(AUB) + P(A) + P(B) in general. Write down and prove the formula for the probability of the union of two sets.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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