In a business, the Chief Executive Officer wants to know if his workers are for or against mandatory vaccinations. A random sample of 200 workers was taken and the results are shown in the MINITAB output below. Expected counts are printed below observed counts Managers Team leaders Employees Total Approve 17 22 15 21.330 17.820 14.850 54 Against 34 25 14 28.835 24.090 20.075 73 No Opinion 28 19 26 28.835 24.090 20.075 73 Total 79 66 55 200 Chi-sq = 0.878992 + 0.980494 + 0.001515 + 0.925168+ 0.034375 + 1.838387 + 0.02418 + 1.075471 + 1.74874 =7.507306 i. What is the value of the degree of freedom for this test? ii. What is the p-value for this test? iii. Carefully define the null and alternative hypotheses of the χ2 test underlying the generation of the above table.
In a business, the Chief Executive Officer wants to know if his workers are for or against
mandatory vaccinations. A random sample of 200 workers was taken and the results are shown
in the MINITAB output below.
Expected counts are printed below observed counts
Managers Team leaders Employees Total
Approve 17 22 15
21.330 17.820 14.850 54
Against 34 25 14
28.835 24.090 20.075 73
No Opinion 28 19 26
28.835 24.090 20.075 73
Total 79 66 55 200
Chi-sq = 0.878992 + 0.980494 + 0.001515 +
0.925168+ 0.034375 + 1.838387 +
0.02418 + 1.075471 + 1.74874 =7.507306
i. What is the value of the degree of freedom for this test?
ii. What is the p-value for this test?
iii. Carefully define the null and alternative hypotheses of the χ2
test underlying the generation of the above table.
iv. Using α = 10%, what is the conclusion of this test? Give reasons for your answer
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