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 the5%significance level, whether an association exists between the specified pair of variables.

income and response

Short answer

The null hypothesis is rejected at 5% level.
Thus, there is an association exists between income and response at the 5% significance level.

Step-by-step solution

Step 1. Given information

An association exists between the specified pair of variables income and response

The given significance$=5\%$

Step 2. Check whether there is an association exists between the specified pair of variables or not.

The hypotheses are given below:
Null hypothesis:
H₀ : There is no association exists between income and response.
Alternative hypothesis:
H₁ : There is an association exists between income and response.

Step 3. Use MINITAB to obtain the test statistic and p-value. 

MINITAB procedure:
Step 1: Choose Stat > Tables > Chi-Square test for association.
Step 2: In Columns containing the table, enter the column of Under $\$20,000,\$20,000-\$29,999,\$30,000-\$49,999$and $\$60,000$and over.
Step 3: In Rows, select Response.
Step 4: Under Statistics, select Chi-square test, Display counts in each cell, Display marginal counts and expected cell counts.
Step 5: Click OK.

Step 4. MINTAB output

chi-square test for Association:RESPONSE,Worksheet columns

From the MINITAB output,the value of the chi-square statistic is$16.634$and the p-value is$0.011$

Step 5. Conclusion for the given question

Here, theP-value is lesser than the level of significance.
That is,P-value $\left(=0.011\right)<\alpha =\left(=0.05\right)$.
Therefore, the null hypothesis is rejected at5%level.
Thus, there is an association exists between income and response at the5%significance level.