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.

age 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 age 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= age 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 age and response.
Alternative hypothesis:
H₁ : There is an association exists between age and response.

Step 3.  Finding 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 18-29 years,30−49years, 50-64 years and 65 and older.
Step 3: Click OK.

Step 5. Finding the MINITAB output

Chi-square test for $18-29$years,$30-49$years,$50-64$years, $65$and above

From the MINITAB output,the value of the chi-square statistic is$41.430$

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

From the MINITAB output, the P-value is$0.000$

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$(=0.000)<\alpha (=0.05).$
Therefore, the null hypothesis is rejected at$5\%$level.
Thus, the results are statistically significant at$5\%$level of significance.

Interpretation:
Thus, there is an association exists between age and response at the $5\%$significance level.