Question

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. [2]

b) Carefully define the null and alternative hypotheses of the Chi Square test

underlying the generation of the above table.

Answer 1

a)

The random variables are age employee and department where employee works.

b)

the null hypothesis:

$H_0:$ age employee and department where employee works are independent.

the alternative hypothesis:

$H_a:$ age employee and department where employee works are dependent.