Explanation Consider the following scenario, “A factory worker’s union is appealing to the factory management for more vacation time for its employees. The union claims that workers are more productive when they come back from vacation than before.” The following table conatians the production rates, measured in units per hour, for a sample of employees is, Production Rates 100-125 Units per Hour 126-150 Units per Hour More Than 150 Units per Hour Total Before Vacation 210 Workers 319 Workers 58 Workers 587 After Vacation 178 Workers 387 Workers 60 Workers 625 total 388 706 118 1212 Step 1: To state the null and alternative hypotheses. Let the null hypothesis be that production rates and vacation status are independent of one another. Null hypothesis: H 0 : Production rates and vacation status are independent. Alternative hypothesis: H a : Production rates and vacation status are dependent. Step 2: To determine which distribution to use for the test statistic, and state the level of significance. To determine there is a relationship between production rates and vacation status. Since we assume that the necessary condition that have been met. So, use the chi-square test for this association and the level of siginificance is α = 0.01 . Step 3: To calculate the test statistic. First calculate the expected value for each cell in the contingency table . Formula for calculating expected value of a frequency in a contingency table: The expected value of the frequency for the i th possible outcome in a contingency table is given by E i = ( r o w t o t a l ) ( c o l u m n t o t a l ) n Where n is the sample size . From the above table represent the value of n is 1212. The expected values of for before vacation and production rates is given below, E b e f o r e v a c c a t i o n a n d 100 − 125 U n i t s p e r H o u r = 587 × 388 1212 = 227756 1212 = 187.9175 E b e f o r e v a c c a t i o n a n d 126 − 150 U n i t s p e r H o u r = 587 × 706 1212 = 414422 1212 = 341.9323 E b e f o r e v a c c a t i o n a n d M o r e T h a n 150 U n i t s p e r H o u r = 587 × 118 1212 = 69266 1212 = 57.1502 The expected values of for after vacation and production rates is given below, E a f t e r v a c c a t i o n a n d 100 − 125 U n i t s p e r H o u r = 625 × 388 1212 = 242500 1212 = 200.0825 E a f t e r v a c c a t i o n a n d 126 − 150 U n i t s p e r H o u r = 625 × 706 1212 = 441250 1212 = 364.0677 E a f t e r v a c c a t i o n a n d M o r e T h a n 150 U n i t s p e r H o u r = 625 × 118 1212 = 73750 1212 = 60.8498 The table represents the contingency table of expected values by using the above formula is given below, Expected Values 100-125 Units per Hour 126-150 Units per Hour More Than 150 Units per Hour Total Before Vacation 187.9175 341.9323 57.15017 587 After Vacation 200.0825 364.0677 60.84983 625 total 388 706 118 1212 Formula for calculating test statistic for a Chi-Square test for association: The test statistic for a chi-square test for association is given below, χ 2 = ∑ i = 1 n ( O i − E i ) 2 E i Where O i , is the observed frequency for the i th possible outcome and E i is the expected frequency for the i th possible outcome and n is the sample size. From the above table represent the value of n is 926. The test statistic, χ 2 , for a chi- square test for association using the above contingency tables is given below,

2nd Edition

ISBN: 9781932628678

Author: Carolyn Warren; Kimberly Denley; Emily Atchley

Publisher: Hawkes Learning Systems

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Chapter 10 Solutions

Beginning Statistics, 2nd Edition

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.2 - Prob. 27E Ch. 10.2 - Prob. 28E Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - Prob. 3E Ch. 10.3 - Prob. 4E Ch. 10.3 - Prob. 5E Ch. 10.3 - Prob. 6E Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.4 - Prob. 1E Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - Prob. 7E Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.5 - Prob. 1E Ch. 10.5 - Prob. 2E Ch. 10.5 - Prob. 3E Ch. 10.5 - Prob. 4E Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Prob. 9E Ch. 10.5 - Prob. 10E Ch. 10.5 - Prob. 11E Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.6 - Prob. 1E Ch. 10.6 - Prob. 2E Ch. 10.6 - Prob. 3E Ch. 10.6 - Prob. 4E Ch. 10.6 - Prob. 5E Ch. 10.6 - Prob. 6E Ch. 10.6 - Prob. 7E Ch. 10.6 - Prob. 8E Ch. 10.6 - Prob. 9E Ch. 10.6 - Prob. 10E Ch. 10.6 - Prob. 11E Ch. 10.6 - Prob. 12E Ch. 10.6 - Prob. 13E Ch. 10.6 - Prob. 14E Ch. 10.6 - Prob. 15E Ch. 10.6 - Prob. 16E Ch. 10.6 - Prob. 17E Ch. 10.6 - Prob. 18E Ch. 10.6 - Prob. 19E Ch. 10.6 - Prob. 20E Ch. 10.6 - Prob. 21E Ch. 10.6 - Prob. 22E Ch. 10.6 - Prob. 23E Ch. 10.6 - Prob. 24E Ch. 10.6 - Prob. 25E Ch. 10.6 - Prob. 26E Ch. 10.7 - Prob. 1E Ch. 10.7 - Prob. 2E Ch. 10.7 - Prob. 3E Ch. 10.7 - Prob. 4E Ch. 10.7 - Prob. 5E Ch. 10.7 - Prob. 6E Ch. 10.7 - Prob. 7E Ch. 10.7 - Prob. 8E Ch. 10.7 - Prob. 9E Ch. 10.7 - Prob. 10E Ch. 10.7 - Prob. 11E Ch. 10.7 - Prob. 12E Ch. 10.7 - Prob. 13E Ch. 10.7 - Prob. 14E Ch. 10.7 - Prob. 15E Ch. 10.7 - Prob. 16E Ch. 10.7 - Prob. 17E Ch. 10.7 - Prob. 18E Ch. 10.7 - Prob. 19E Ch. 10.7 - Prob. 20E Ch. 10.CR - Prob. 1CR Ch. 10.CR - Prob. 2CR Ch. 10.CR - Prob. 3CR Ch. 10.CR - Prob. 4CR Ch. 10.CR - Prob. 5CR Ch. 10.CR - Prob. 6CR Ch. 10.CR - Prob. 7CR Ch. 10.CR - Prob. 8CR Ch. 10.CR - Prob. 9CR Ch. 10.CR - Prob. 10CR Ch. 10.CR - Prob. 11CR Ch. 10.CR - Prob. 12CR Ch. 10.CR - Prob. 13CR Ch. 10.CR - Prob. 14CR Ch. 10.CR - Prob. 15CR Ch. 10.P - Prob. 1P Ch. 10.P - Prob. 2P Ch. 10.P - Prob. 3P Ch. 10.P - Prob. 4P Ch. 10.P - Prob. 5P Ch. 10.P - Prob. 6P Ch. 10.P - Prob. 7P Ch. 10.P - Prob. 8P Ch. 10.P - Prob. 9P Ch. 10.P - Prob. 10P

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Chapter 10 Solutions

To find:

To calculate the test statistic.