Employees of Axolotl Corporation were sampled at random from pay records and asked to complete an anonymous job satisfaction survey, yielding the tabulation shown. Research question: at a=. 05, is job satisfaction independent of pay category?
Employees;
Step 1: State the Hypotheses
Job satisfaction is independent of pay category.
Job satisfaction is dependent of pay category.
Step 2: State the Decision Rule
For the pay records contingency table,
r = 2 rows, and c = 3 columns. Therefore degree of freedom is
df = (r – 1)(c – 1) = (2 – 1)(3 – 1) = 2
At α = 0. 05 and df = 2 , the right-tail critical value is 5. 991.
For α = 0. 05in a right-tailed test, the decision rule is:
Reject if > 5. 991. Otherwise, do not reject.
Step 3: Calculate the Expected Frequencies
The expected frequency in row j and column k is
Step 4: Calculate the Test Statistic
Using Excel MegaStat, The chi-square test statistic is = 4. 54.
Step 5: Make the Decision
The test statistic = 4. 54 is less than the critical value 5. 991.
Decision: Do not reject .
This is also confirmed by p-value (0. 1032).
At level of significance, α = 0. 05, the data provide sufficient evidence to conclude that job satisfaction is independent of pay category.
