Answer to Question #260948 in Statistics and Probability for bri

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. 

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. [2]

Answer 1

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.

The expected count for each cell:

$df=(r-1)(c-1)=(4-1)(4-1)=9$

critical value:

$\chi^2_{crit}=16.919$

Since $\chi^2=80.395>\chi^2_{crit}$ , we reject the null hypothesis.

Age employee and department where employee works are dependent.