Employees of Axolotl Corporation
- Pages: 2
- Word count: 333
- Category: Corporation Graphic
A limited time offer! Get a custom sample essay written according to your requirements urgent 3h delivery guaranteed
Order NowEmployees 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;
| Satisfied | neutral | dissatisfied | total | |
| Pay type salaried | 20 | 13 | 2 | 35 |
| Hourly | 135 | 127 | 58 | 320 |
| Total | 155 | 140 | 60 | 355 |
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
| Satisfied | Neutral | Dissatisfied | Total | ||
| Pay type salaried | Observed | 20 | 13 | 2 | 35 |
| Expected | 15.28 | 13.80 | 5.92 | 35.00 | |
| Hourly | Observed | 135 | 127 | 58 | 320 |
| Expected | 139.72 | 126.20 | 54.08 | 320.00 | |
| Total | Observed | 155 | 140 | 60 | 355 |
| Expected | 155.00 | 140.00 | 60.00 | 355.00 |
Step 4: Calculate the Test Statistic
Using Excel MegaStat, The chi-square test statistic is = 4.54.
| Chi-square Contingency Table Test for Independence | ||||||
| Satisfied | Neutral | Dissatisfied | Total | |||
| Pay type salaried | Observed | 20 | 13 | 2 | 35 | |
| Expected | 15.28 | 13.80 | 5.92 | 35.00 | ||
| O – E | 4.72 | -0.80 | -3.92 | 0.00 | ||
| (O – E)² / E | 1.46 | 0.05 | 2.59 | 4.10 | ||
| Hourly | Observed | 135 | 127 | 58 | 320 | |
| Expected | 139.72 | 126.20 | 54.08 | 320.00 | ||
| O – E | -4.72 | 0.80 | 3.92 | 0.00 | ||
| (O – E)² / E | 0.16 | 0.01 | 0.28 | 0.45 | ||
| Total | Observed | 155 | 140 | 60 | 355 | |
| Expected | 155.00 | 140.00 | 60.00 | 355.00 | ||
| O – E | 0.00 | 0.00 | 0.00 | 0.00 | ||
| (O – E)² / E | 1.62 | 0.05 | 2.88 | 4.54 | ||
| 4.54 | chi-square | |||||
| 2 | df | |||||
| .1032 | p-value | |||||
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.
