Question

Inference recap ($8.1$to $11.2$) In each of the following settings, state which inference procedure from Chapter $8,9,10,or11$you would use. Be specific. For example, you might answer, “Two-sample z test for the difference between two proportions.” You do not have to carry out any procedures.

a. Is there a relationship between attendance at religious services and alcohol consumption? A random sample of $1000$adults was asked whether they regularly attend religious services and whether they drink alcohol daily.

b. Separate random samples of $75$ college students and $75$ high school students were asked how much time, on average, they spend watching television each week. We want to estimate the difference in the average amount of TV watched by high school and college students.

Short answer

a. Chi-square test of independence should be used.

b. The t- test for two sample for the mean difference should be used.

Step-by-step solution

Part (a) Step 1 : Given information

We have to explain which test will be applicable from inference.

Part (a) Step 2 : Simplification

Is there a link between attending religious services and consuming alcoholic beverages? A random sample of
$1000$ persons were questioned if they attended religious services on a regular basis and drank alcohol on a daily basis.

First, we must make a list of the hypothesis tests that we have learned.

For a single sample, the Z-test or proportion interval is used. For two samples, the Z-test or proportion interval is used. T-test or mean interval for a single sample. T-test or mean interval for two samples. Mean paired t-test for two samples. The Chi-square test for homogeneity or independence.

For instance, the association between religious attendance and alcohol intake should be investigated.

As a result, the chi-square independence test should be used.

Part (b) Step 1 : Given information

We have to explain which test will be applicable from inference.

Part (b) Step 2 : Simplification

College students $75$and $75$high school students were randomly selected and asked how much time they spent watching television on a weekly basis.

We'dwanttocalculatethedifferenceinaverageTVviewingtimebetweenhighschoolandcollegestudents.

First, we must make a list of the hypothesis tests that we have learned. For a single sample, the Z-test or proportion interval is used. For two samples, the Z-test or proportion interval is used. T-test or mean interval for a single sample. T-test or mean interval for two samples. Mean paired t-test for two samples.

TheChi-squaretestforhomogeneityorindependence.

Check the difference between two averages of two samples in the provided example.

As a result, a two-sample t-test for the mean difference should be utilized.