Question

4. The following table shows the number of people employed or not based on their college major. Determine if college major is independent of employment or not. Set alpha = .05

                                                            Employed                   Not employed                    Total

Technical Science Degree                       10                                       2                           12

Social Science Degree                                         7                                         3                         10

Visual Arts Degree                                  5                                         5                           10

Total                                                        22                                       10                            32

Step 1: State the null and research hypotheses in words.                              (2 points)

Step 2: Find the critical value                                                                       (1 point)

Step 3: Compute the appropriate test statistic                                               (4 points)

Step 4: Evaluate the null. Reject or Fail to Reject?                                     (1 point)

Step 5: What is your conclusion?                                                                 (1 point)

Answer 1

H :college major is independent of employment H:college major is dependent of employment Significance level: a = 0.05 Degree of freedom: df =r-1XC-1 = (3-1)×(2-1) = 2 Critical value: Using the chi square table, the critical value at 5% level of significance for a right tailed test is, Los =5.991 Test statistic: χ =Σ 760-E) E Where, O =Observed counts. E = Expected counts

The formula for calculating the expected counts is, Row total x column total E = Grand total The below table describes the computation of chi square test statistic: Technical science degree Observed Expected O-E (0 - E2/E Social science degree Observed Expected O-E (O - E)? / E Visual arts degree Observed Expected O-E (0-E)? / E Total Observed Expected O-E (0 - E) / E Employed Not employed 10 2 8.25 3.75 1.75 -1.75 0.37 0.82 7 3 6.88 3.13 0.13 -0.13 0.00 0.01 5 5 6.88 3.13 -1.88 1.88 0.51 1.13 22 10 22.00 10.00 0.00 0.00 0.88 1.95 x = 2.83 Total 12 12.00 0.00 1.19 10 10.00 0.00 0.01 10 10.00 0.00 1.64 32 32.00 0.00 2.83 Therefore, the chi-square test statistic is

Decision rule : Reject H if x > xã otherwise do not reject H. Since the test statistic value is less than critical value, so we fail to reject the null hypothesis at the specified level of significance Conclusion: There is not sufficient evidence to warrant the rejection of the claim that college major independent of employment