Answer to Question #282997 in Statistics and Probability for Job

Question

The director of a large firm wants to determine the opinion of various groups of employee towards a proposed performance evaluation method. A random sample of 100 employees from the finance ,50 employees from production and 50 employees from personal department is saved with the following results.

Opinion Finance Production Personnel

Favor 63 27 30

Oppose 37 23 20

Totals 100 50 50

At the 0.01 level of significance, is there evidence in attitude the method between various department

Answer 1

Chi-square test is performed to check attitude towards evaluation method between various department. Following steps are taken to perform chi-square test:

Step 1: Null and Alternative Hypothesis

H₀: Employees' opinion concerning the proposed evaluation method between various department is independent

H₁: Employees' opinion concerning the proposed evaluation method between various department is independent

Step 2: Calculation of Test Statistic

Following formula is used to calculate chi-square statistic:

$\chi^2=\Sigma \frac{(Observed - Expected)^2}{Expected}$

But, firstly needs to calculate expected frequency using following formula:

$E=\frac{RT\times CT}{GT}$

$E(Favor-to-Finance)=\frac{100\times 120}{200}=60$

$E(Favor-to-Production)=\frac{50\times 120}{200}=30$

$E(Favor-to-Personnel)=\frac{50\times 120}{200}=30$

$E(Oppsoe-to-Finance)=\frac{100\times 80}{200}=40$

$E(Oppose-to-Production)=\frac{50\times 80}{200}=20$

$E(Oppose-to-Personnel)=\frac{50\times 80}{200}=20$

Then, chi-square test statistic is:

$\chi^2=\frac{(63 - 60)^2}{60}+\frac{(27- 30)^2}{30}+\frac{(30- 30)^2}{30}+\frac{(37- 40)^2}{40}+\frac{(23- 20)^2}{20}+\frac{(20- 20)^2}{20}$

$\chi^2=1.125$

Step 3: Critical Value

Degree of freedom = (2 - 1)*(3 - 1) = 2

As per the chi-square distribution, critical value in respect to degree of freedom of 2 and 0.01 level of significance is 9.21.

Step 4: Statistical Decision

Since, chi-square test statistic is less than critical value (1.125 < 9.21). So, we can't reject null hypothesis.

Step 5: Conclusion

It can conclude that employee's opinions concerning the proposed performance evaluation method between various departments are independent.