The human resource manager at a car dealership wants to know if the ages of its employees are related to the department that they work in. Data was compiled and tabulated in a 2-way contingency table. The employees were classified according to their age and department. Expected counts are printed below observed counts Sales Accounts Marketing Repairs Total 20-29 8 10 27 43 88 17.74 *** 26.20 23.62 30-39 29 26 38 22 * 23.18 26.72 34.24 30.86 40-49 33 32 72 82 219 44.15 50.88 65.20 58.77 50-59 81 106 86 54 327 65.92 75.97 97.36 87.75 Total 151 ** 223 201 749 Chi-Sq = 5.348 + **** + 0.024 + 15.912 + 1.459 + 0.019 + 0.413 + 2.544 + 2.816 + 7.003 + 0.709 + 9.182 + 3.448 + 11.875 + 1.325 + 12.983 = 80.395 DF = *****, P-Value = ****** No cells with expected counts less than 5. a) Name the random variables present in the table above. b) Carefully define the null and alternative hypotheses of the Chi Square test underlying the generation of the above table. c) Fill in the gaps marked by ‘*’, ‘**’, ‘***’, ‘****’ , ‘*****’ and ‘******’ [8] 8 d) What is the assumption on which these calculations are based? e) What is relevance of the statement” No cells with expected counts less than 5.” f) Do the records suggest a relationship or independence between age and department for the employees of this car dealership at the 5% significance level? Give reason(s) for your answer.
The human resource manager at a car dealership wants to know if the ages of its employees are related to the department that they work in. Data was compiled and tabulated in a 2-way contingency table. The employees were classified according to their age and department.
Expected counts are printed below observed counts
Sales Accounts Marketing Repairs
Total
20-29 8 10 27 43 88
17.74 *** 26.20 23.62
30-39 29 26 38 22 *
23.18 26.72 34.24 30.86
40-49 33 32 72 82 219
44.15 50.88 65.20 58.77
50-59 81 106 86 54 327
65.92 75.97 97.36 87.75
Total 151 ** 223 201 749
Chi-Sq = 5.348 + **** + 0.024 + 15.912 + 1.459 + 0.019 + 0.413 + 2.544 +
2.816 + 7.003 + 0.709 + 9.182 + 3.448 + 11.875 + 1.325 + 12.983 = 80.395
DF = *****, P-Value = ******
No cells with expected counts less than 5.
a) Name the random variables present in the table above.
b) Carefully define the null and alternative hypotheses of the Chi Square test underlying the generation of the above table.
c) Fill in the gaps marked by ‘*’, ‘**’, ‘***’, ‘****’ , ‘*****’ and ‘******’ [8]
8
d) What is the assumption on which these calculations are based?
e) What is relevance of the statement” No cells with expected counts less than 5.”
f) Do the records suggest a relationship or independence between age and
department for the employees of this car dealership at the 5% significance level?
Give reason(s) for your answer.
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