An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 13.2, Problem 1Q
In recent years a number of research projects in extrasensory perception have examined the possibility that hypnosis may be helpful in bringing out ESP in persons who did not think they had any. The obvious way to test such a hypothesis is with a self-paired design: the ESP ability of a subject when he is awake is compared to his ability when hypnotized. In one study of this sort, fifteen college students were each asked to guess the identity of two hundred Zener cards (see Case Study 4.3.1). The same “sender”-that is, the person concentrating on the card-was used for each trial. For one hundred of the trials both the student and the sender were awake; for the other one hundred both were hypnotized. If chance were the only factor involved, the expected number of correct identifications in each set of one hundred trials would be twenty. The observed average numbers of correct guesses for subjects awake and subjects hypnotized were 18.9 and 21.7, respectively (24). Use the analysis of variance to determine whether that difference is statistically significant at the 0.05 level.
| Number of Correct Responses (out of 100) in ESP Experiment | ||
| Student | Sender and Student In Waking State | Sender and Student In Hypnotic state |
| 1 | 18 | 25 |
| 2 | 19 | 20 |
| 3 | 16 | 26 |
| 4 | 21 | 26 |
| 5 | 16 | 20 |
| 6 | 20 | 23 |
| 7 | 20 | 14 |
| 8 | 14 | 18 |
| 9 | 11 | 18 |
| 10 | 22 | 20 |
| 11 | 19 | 22 |
| 12 | 29 | 27 |
| 13 | 16 | 19 |
| 14 | 27 | 27 |
| 15 | 15 | 21 |
| 16 | 18.9 | 21.7 |
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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).
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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
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Chapter 13 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 13.2 - In recent years a number of research projects in...Ch. 13.2 - Prob. 2QCh. 13.2 - Prob. 3QCh. 13.2 - Prob. 4QCh. 13.2 - Prob. 5QCh. 13.2 - Prob. 6QCh. 13.2 - Prob. 7QCh. 13.2 - Prob. 8QCh. 13.2 - Prob. 9QCh. 13.2 - Prob. 10Q
Ch. 13.2 - Prob. 11QCh. 13.2 - Prob. 12QCh. 13.2 - Prob. 13QCh. 13.3 - Case Study 7.5.2 compared the volatility of Global...Ch. 13.3 - Recall the depth perception data described in...Ch. 13.3 - Useapaired t test to analyze the hypnosis/ESP data...Ch. 13.3 - Prob. 5QCh. 13.3 - Let D1,D2,...,Db be the within-block differences...Ch. 13.3 - Prob. 7QCh. 13.3 - Prob. 8QCh. 13.3 - Prob. 9Q
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