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Employees of Axolotl Corporation Essay Sample

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Employees of Axolotl Corporation Essay Sample

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;

 

  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  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  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.

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