Research Methods for the Behavioral Sciences (MindTap Course List)
5th Edition
ISBN: 9781305104136
Author: Frederick J Gravetter, Lori-Ann B. Forzano
Publisher: Wadsworth Publishing
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Chapter 3, Problem 3E
Briefly explain what an operational definition is and why operational definitions are sometimes necessary.
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5. Let X and Y be independent random variables and let the superscripts denote
symmetrization (recall Sect. 3.6). Show that
(X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose
that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qr (h)).
Chapter 3 Solutions
Research Methods for the Behavioral Sciences (MindTap Course List)
Ch. 3.2 - Define a construct and explain the role that...Ch. 3.2 - Define an operational definition and explain the...Ch. 3.3 - Define a positive relationship and a negative...Ch. 3.3 - Define the validity of measurement and explain why...Ch. 3.3 - Define the reliability of measurement and explain...Ch. 3.4 - Compare and contrast the four scales of...Ch. 3.5 - Identify the three modalities of measurement and...Ch. 3.6 - Define a ceiling effect and a floor effect and...Ch. 3.6 - Define an artifact and explain how examples of...Ch. 3 - In addition to the key words, you should also be...
Ch. 3 - Some variables, such as height, can be measured...Ch. 3 - Briefly explain what an operational definition is...Ch. 3 - A researcher evaluates a new cholesterol...Ch. 3 - A clinical researcher has developed a new test for...Ch. 3 - Suppose that a social scientist has developed a...Ch. 3 - Explain how inter-rater reliability is...Ch. 3 - A researcher claims that intelligence can be...Ch. 3 - Identify the scale of measurement that allows each...Ch. 3 - What is the primary advantage of self-report...Ch. 3 - Describe the strengths and weaknesses of...Ch. 3 - What is a ceiling effect, and how can it be a...Ch. 3 - What are demand characteristics, and how do they...Ch. 3 - Describe how the concept of participant reactivity...Ch. 3 - Select a subject and use a full-text database such...Ch. 3 - Select one construct from the following list:...Ch. 3 - For each of the following operational definitions,...
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- 10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward
- 7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward
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- 2 Make a histogram from this data set of test scores: 72, 79, 81, 80, 63, 62, 89, 99, 50, 78, 87, 97, 55, 69, 97, 87, 88, 99, 76, 78, 65, 77, 88, 90, and 81. Would a pie chart be appropriate for this data? ganizing Quantitative Data: Charts and Graphs 45arrow_forward10 Meteorologists use computer models to predict when and where a hurricane will hit shore. Suppose they predict that hurricane Stat has a 20 percent chance of hitting the East Coast. a. On what info are the meteorologists basing this prediction? b. Why is this prediction harder to make than your chance of getting a head on your next coin toss? U anoiaarrow_forward6. Show that one cannot find independent, identically distributed random variables X and Y such that X-YE U(-1, 1). 7 Consider al onarrow_forward
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