Question

Job Satisfaction. A CNN/USA TODAY poll conducted by Gallul asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among which were gender, age, type of community, educational attainment, income, and type of employer. The data are provided on the WeissStats site. In each of Exercises 12.87-12.92, use the technology of your choice to decide, at the 5% significance level, whether an association exists between the specified pair of variables.

Educational attainment and response

Short answer

The null hypothesis is rejected at 5% level.
The results are statistically significant at 5% level of significance.
There is an association exists between education attainments and response at the 5% significance level.

Step-by-step solution

Step 1. Given information

The given significance level $=5\%$

The given specified pair of variables= educational attainments and response

Step 2. Check whether or not there is association exists between age and response at 5% significance level. 

Step 1:
The test hypotheses are given below:
Null hypothesis:
H₀ : There is no association exists between educational attainment and response.
Alternative hypothesis:
H₁ : There is an association exists between educational attainment and response.

Step 3.  Finding the level of significance

Step 2: Decide the level of significance.
Here, the level of significance is,$\alpha =0.05$

Step 4. Find the expected frequency and test statistic. 

MINITAB procedure:
Step 1: Choose Stat>Tables>Chi-Square Test (Two-Way Table in Worksheet).
Step 2: In Columns containing the table, enter the columns of Postgraduate, College graduate, Some college and No college.
Step 3: Click OK.

Step 5. Finding the MINITAB output 

Chi-Square Test: Postgraduate, College graduate, Some college, No college

From the MINITAB output,the value of the chi-square statistic is$13.651$

Step 6. Finding p-value and check the solution by rejection and interpretation

From the MINITAB output, the P-value is $=0.034$

Rejection rule:
If P-value$\le \alpha$, then reject the null hypothesis.
Here, theP-value is lesser than the level of significance,
That is, P-value$\left(0.034\right)<\alpha =(0.005)$.
Therefore, the null hypothesis is rejected at5%level.
Thus, the results are statistically significant at 5% level of significance.

Interpretation:
Thus, there is an association exists between education attainments and response at the 5% significance level.