Essential Statistics for the Behavioral Sciences
2nd Edition
ISBN: 9781506386300
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
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Chapter 13, Problem 1FP
To determine
To discuss: The concept of
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Explanation of Solution
Correlation is measure of linear association between two variables. The variables are said to be correlated when the change in one variable affects the other variable.
The
If two variables have a very strong positive relation, then the correlation value lies between .8 and 1. If two variables have a strong correlation, then correlation falls between .6 and .8. If two variables have a moderate positive relation, then the correlation value lies between .4 and .6. If two variables have a weak positive relation, then the correlation value lies between .2 and .4. And, if two variables have a very weak positive relation, then the correlation value lies between .0 and .2.
Similarly, if two variables have a very strong negative relation, then the correlation value lies between
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Pam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.Which is a second division that Rob would make of his share of the cake?
Three players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).
If the choosers' declarations are Chooser 1: {s1 , s2} and Chooser 2: {s2 , s3}.
Using the lone-divider method, how many different fair divisions of this cake are possible?
Theorem 2.6 (The Minkowski inequality)
Let p≥1. Suppose that X and Y are random variables, such that E|X|P <∞ and
E|Y P <00. Then
X+YpX+Yp
Chapter 13 Solutions
Essential Statistics for the Behavioral Sciences
Ch. 13 - Prob. 1FPCh. 13 - Prob. 2FPCh. 13 - Prob. 3FPCh. 13 - Prob. 4FPCh. 13 - Prob. 5FPCh. 13 - Prob. 6FPCh. 13 - Prob. 7FPCh. 13 - Prob. 8FPCh. 13 - Prob. 9FPCh. 13 - Prob. 10FP
Ch. 13 - Prob. 11CAPCh. 13 - Prob. 12CAPCh. 13 - Prob. 13CAPCh. 13 - Prob. 14CAPCh. 13 - Prob. 15CAPCh. 13 - Prob. 16CAPCh. 13 - Prob. 17CAPCh. 13 - Prob. 18CAPCh. 13 - Prob. 19CAPCh. 13 - Prob. 20CAPCh. 13 - Prob. 21CAPCh. 13 - Prob. 22CAPCh. 13 - Prob. 23CAPCh. 13 - Prob. 24CAPCh. 13 - Prob. 25CAPCh. 13 - Prob. 26CAPCh. 13 - Prob. 27CAPCh. 13 - Prob. 28CAPCh. 13 - Prob. 29CAPCh. 13 - Prob. 30CAPCh. 13 - Prob. 31CAPCh. 13 - Prob. 32PRCh. 13 - Prob. 33PRCh. 13 - Prob. 34PRCh. 13 - Prob. 35PRCh. 13 - Prob. 36PR
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- Theorem 1.2 (1) Suppose that P(|X|≤b) = 1 for some b > 0, that EX = 0, and set Var X = 0². Then, for 0 0, P(X > x) ≤e-x+1²² P(|X|>x) ≤2e-1x+1²² (ii) Let X1, X2...., Xn be independent random variables with mean 0, suppose that P(X ≤b) = 1 for all k, and set oσ = Var X. Then, for x > 0. and 0x) ≤2 exp Σ k=1 (iii) If, in addition, X1, X2, X, are identically distributed, then P(S|x) ≤2 expl-tx+nt²o).arrow_forwardTheorem 5.1 (Jensen's inequality) state without proof the Jensen's Ineg. Let X be a random variable, g a convex function, and suppose that X and g(X) are integrable. Then g(EX) < Eg(X).arrow_forwardCan social media mistakes hurt your chances of finding a job? According to a survey of 1,000 hiring managers across many different industries, 76% claim that they use social media sites to research prospective candidates for any job. Calculate the probabilities of the following events. (Round your answers to three decimal places.) answer parts a-c. a) Out of 30 job listings, at least 19 will conduct social media screening. b) Out of 30 job listings, fewer than 17 will conduct social media screening. c) Out of 30 job listings, exactly between 19 and 22 (including 19 and 22) will conduct social media screening. show all steps for probabilities please. answer parts a-c.arrow_forward
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- Theorem 7.2 Suppose that E X = 0 for all k, that Var X = 0} x) ≤ 2P(S>x 1≤k≤n S√2), -S√2). P(max Sk>x) ≤ 2P(|S|>x- 1arrow_forwardThree players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).If the chooser's declarations are Chooser 1: {s3} and Chooser 2: {s3}, which of the following is a fair division of the cake?arrow_forwardTheorem 1.4 (Chebyshev's inequality) (i) Suppose that Var X x)≤- x > 0. 2 (ii) If X1, X2,..., X, are independent with mean 0 and finite variances, then Στη Var Xe P(|Sn| > x)≤ x > 0. (iii) If, in addition, X1, X2, Xn are identically distributed, then nVar Xi P(|Sn> x) ≤ x > 0. x²arrow_forwardTheorem 2.5 (The Lyapounov inequality) For 0arrow_forwardTheorem 1.6 (The Kolmogorov inequality) Let X1, X2, Xn be independent random variables with mean 0 and suppose that Var Xk 0, P(max Sk>x) ≤ Isk≤n Σ-Var X In particular, if X1, X2,..., X, are identically distributed, then P(max Sx) ≤ Isk≤n nVar X₁ x2arrow_forwardTheorem 3.1 (The Cauchy-Schwarz inequality) Suppose that X and Y have finite variances. Then |EXYarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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