Question

Tuition bills A random sample of U.S. adults was recently asked, “Would you support or oppose major new spending by the federal government that would help undergraduates pay tuition at public colleges without needing loans?” The two-way table shows the responses, grouped by age.

Do these data provide convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults?

Short answer

Yes, these data provide convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults.

Step-by-step solution

 Step 1: Given information 

We havew to tell about convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults.

Explanation 

The significamce level of $\alpha$is $0.05$.

The age of the respondent has no bearing on the response.

The expected frequencies are:

$E_{11}=\frac{r_1\times c_1}{n}=\frac{856\times 120}{1509}\approx 68.07$

Finally, after determining all of the other characteristics, we arrive at

$E_{34}=\frac{r_3\times c_4}{n}=\frac{88\times 638}{1509}\approx 37.21$

Hypothesis Test:

${\chi }^2=\sum \frac{(O-E{)}^2}{E}$

Using the above formula we get $=39.74$

$P<0.05\Rightarrow \text{Reject}{H}_0$

There is evidence to suggest that there is a link between age and response.