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solutions9

# solutions9 - ISDS Homework 9 Solutions Panayiotis Skordi...

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ISDS Homework 9 - Solutions Chi-Square Hypothesis Testing Panayiotis Skordi 1. The president of a large university has been studying the relationship between male/female supervisory structures in his institution and the level of employees’ job satisfaction. The results of a recent survey are shown in the table below. Conduct a test at the 5% significance level to determine whether the level of job satisfaction depends on the boss/employee gender relationship. Boss/ Employee Level of Satisfaction Male/Female Female/Male Male/Male Female/Female Satisfied 60 15 50 15 Neutral 27 45 48 50 Dissatisfied 13 32 12 55 ANSWER H 0 : Level of job satisfaction and the boss/employee gender relationship are independent Question 1 H 1 :Level of job satisfaction and the boss/employee gender relationship are dependent. OBSERVED,O Male/Female Female/Male Male/Male Female/Female Satisfied 60 15 50 15 140 Neutral 27 45 48 50 170 Dissatisfied 13 32 12 55 112 100 92 110 120 422 EXPECTED,E Male/Female Female/Male Male/Male Female/Female Satisfied 140*100/422 140*92/422 140*110/422 140*120/422 140 Neutral 170*100/422 170*92/422 170*110/422 170*120/422 170 Dissatisfied 112*100/422 112*92/422 112*110/422 112*120/422 112 100 92 110 120 422 ,E Male/Female Female/Male Male/Male Female/Female Satisfied 33.1754 30.5213 36.4929 39.8104 140 Neutral 40.2844 37.0616 44.3128 48.3412 170 Dissatisfied 26.5403 24.4171 29.1943 31.8483 112 100 92 110 120 422 O - E Male/Female Female/Male Male/Male Female/Female Satisfied 26.8246 -15.5213 13.5071 -24.8104 Neutral -13.2844 7.9384 3.6872 1.6588 Dissatisfied -13.5403 7.5829 -17.1943 23.1517 1

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(O - E) 2 Male/Female Female/Male Male/Male Female/Female Satisfied 719.5616 240.9116 182.4420 615.5573 Neutral 176.4742 63.0180 13.5955 2.7515 Dissatisfied 183.3393 57.5010 295.6444 535.9993 (O - E) 2 /E Male/Female Female/Male Male/Male Female/Female Satisfied 21.6896 7.8932 4.9994 15.4622 50.0445 Neutral 4.3807 1.7004 0.3068 0.0569 6.4448 Dissatisfied 6.9080 2.3549 10.1268 16.8297 36.2194 92.7087 Test Statistic χ 2 = Σ (O – E) 2 = 92.7087 E Critical, cut off point χ 2 c =12.5916 From Tables d.f. = (r – 1)(c – 1) Where: r = the number of rows in the contingency table c = the number of columns in the contingency table. There are 3 rows, r, and 4 columns ,c . So d.f. = (r – 1)(c – 1) = (3- 1)(4 – 1) = 6, and if α = 0.05 χ 2 c = 12.5916 from the χ 2 tables. Reject H 0 Do Not Reject H 0 12.5916 The graph shows the calculated test statistic falling in the “Reject H 0 ” region. So YES, the level of job satisfaction depends on the boss/employee relationship. 2
2. A large carpet store wishes to determine if the brand of carpet purchased is related to the purchaser’s family income. As a sampling frame, they mailed a survey to people who have a store credit card. Five hundred customers returned the survey and the results follow: Brand of Carpet At the 5% level of significance, can you conclude that the brand of carpet purchased is related to the purchaser’s family income? ANSWER H 0 : Family income and brand of carpet purchased are independent Question 2 H 1 : Family income and brand of carpet purchased are dependent. OBSERVED,O Brand A Brand B Brand C High Income 65 32 32 129 Middle Income 80 68 104 252 Low Income 25 35 59 119 170 135 195 500 EXPECTED,E Brand A Brand B Brand C High Income 129*170/500 129*135/500 129*195/500 129 Middle Income 252*170/500 252*135/500 252*195/500 252 Low Income 119*170/500 119*135/500 119*195/500 119 170 135 195 500 ,E Brand A Brand B Brand C High Income 43.8600 34.8300 50.3100 129 Middle Income 85.6800 68.0400 98.2800 252 Low Income 40.4600 32.1300 46.4100 119 170 135 195 500 O - E Brand A Brand B Brand C High Income 21.1400 -2.8300 -18.3100

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solutions9 - ISDS Homework 9 Solutions Panayiotis Skordi...

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