Question

A CNN/USA Today poll conducted by Gallup 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 Exercise \(12.87-12.92\), 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 data provide is sufficient evidence to conclude that an association exist between age and response.

Step-by-step solution

Step 1. Given information

The level of significance \(\alpha =0.05\)

Step 2. Calculation

Consider the below test hypothesis.

Null hypothesis:

\(H_{0}\): There is no association exist between age and response..

Alternative hypothesis:

\(H_{a}\): There is association exist between age and response.

By using any software perform the chi-square homogeneity test to find the test statistic.

Enter the given data,

Then we get, the chi-square static as \(=41.430, p-value=0.00\)

Then, we have the

The rejection rule:

\(p-value \leq \alpha\), then null hypothesis rejected.

The level of significance \(\alpha =0.05\)

Here , clearly \(p-\)value is less than the level of significance.

\(p-value (0.00)<\alpha (0.05)\)

So, the null hypothesis is rejected at \(5%\) significant level.

Thus the results are statistically significant at \(5%\) significant level.

Hence,

The data provide is sufficient evidence to conclude that an association exist between age and response.