Explanation Given info: The data shows the two-way contingency table for the results obtained by using the polygraph. A polygraph is a device used to test whether a person is lying or not. The row represents the test results obtained from the polygraph and the column represents the number of subjects who actually lied or not. Calculation: The claim is to test whether the subject lies is independent from the polygraph test results. If the claim is false, then the subject lies is dependent to polygraph test results. The hypotheses are given below: Null hypothesis: H 0 : The subject lies and polygraph test results are independent of each other. Alternative hypothesis: H 1 : The subject lies and polygraph test results are dependent of each other. The test statistic is calculated by the formula, χ 2 = ∑ ( O − E ) 2 E Where, O represents the observed frequency and E represents the expected frequency Row total, column total and grand total are given as follows: Did the Subject Actually Lie? Total No (Did not lie) Yes (Lied) Polygraph tests positive 15 42 57 Polygraph tests negative 32 9 41 Total 47 51 98 Expected frequency is calculated by using the formula, E = ( Row total ) ( Column total ) ( Grand total ) Where, row total represents the sum of the frequencies along each row, the column total represents the sum of the frequencies along each column and the grand total represents the sum of all frequencies. Expected frequency for the cell E 11 E 11 = ( Row total ) ( Column total ) ( Grand total ) = ( 57 ) ( 47 ) 98 = 2 , 679 98 = 27.3 Expected frequency for the cell E 12 E 12 = ( Row total ) ( Column total ) ( Grand total ) = ( 57 ) ( 51 ) 98 = 2 , 907 98 = 29.7 Expected frequency for the cell E 21 E 21 = ( Row total ) ( Column total ) ( Grand total ) = ( 47 ) ( 41 ) 98 = 1 , 927 98 = 19

13th Edition

ISBN: 9780134462455

Author: Mario F. Triola

Publisher: PEARSON

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Question

Chapter 11.2, Problem 5BSC

To determine

To test: Whether the subject lies is independent from the polygraph test results.

To suggest: The effectiveness of polygraphs for differentiating truths and lies.

Expert Solution & Answer

Chapter 11 Solutions

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Knowledge Booster

To test: Whether the subject lies is independent from the polygraph test results. To suggest: The effectiveness of polygraphs for differentiating truths and lies.

Solution Summary: The author explains the two-way contingency table for the results obtained by using the polygraph. If the claim is false, then the subject lies.

To test: Whether the subject lies is independent from the polygraph test results. To suggest: The effectiveness of polygraphs for differentiating truths and lies.

Chapter 11 Solutions

To test: Whether the subject lies is independent from the polygraph test results.

To suggest: The effectiveness of polygraphs for differentiating truths and lies.