Explanation Given info: A study was conducted between texting while driving and irregular seat belt usage. The results are given below: Irregular Seat Belt Usage Yes No Texting While Driving 1,737 2,048 No Texting While Driving 1,945 2,775 Calculation: The claim is to test whether texting while driving is independent of irregular seat belt usage. If the claim is false, then there is a dependency between texting while driving and irregular seat belt usage. The hypotheses are given below: Null hypothesis: H 0 : Texting while driving is independent of irregular seat belt usage. Alternative hypothesis: H 1 : Texting while driving is dependent of irregular seat belt usage. The test statistic is calculated by using the below 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: Irregular Seat Belt Usage Yes No Row total Texting While Driving 1,737 2,048 3,785 No Texting While Driving 1,945 2,775 4,720 Column total 3,682 4,823 8,505 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 ) = ( 3 , 785 ) ( 3 , 682 ) ( 1 , 737 + 2 , 048 + 1 , 945 + 2 , 775 ) = 13 , 936 , 370 8 , 505 = 1 , 638.6 Expected frequency for the cell E 12 E 12 = ( Row total ) ( Column total ) ( Grand total ) = ( 3 , 785 ) ( 4 , 823 ) ( 1 , 737 + 2 , 048 + 1 , 945 + 2 , 775 ) = 18 , 255 , 055 8 , 505 = 2 , 146.4 Expected frequency for the cell E 21 E 21 = ( Row total ) ( Column total ) ( Grand total ) = ( 4 , 720 ) ( 3 , 682 ) ( 1 , 737 + 2 , 048 + 1 , 945 + 2 , 775 ) = 17 , 379 , 040 8 , 505 = 2 , 043

Elementary Statistics, Books A La Carte Edition (13th Edition)

13th Edition

ISBN: 9780134463063

Author: Mario F. Triola

Publisher: PEARSON

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Question

Chapter 11.2, Problem 8BSC

To determine

To test: The claim that texting while driving is independent of irregular seat belt usage.

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Chapter 11.2, Problem 7BSC

Chapter 11.2, Problem 9BSC

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Chapter 11 Solutions

Elementary Statistics, Books A La Carte Edition (13th Edition)

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