Q.60 - The Practice of Statistics for AP

Question

Inference recap $(8.1 to 11.2)$ In each of the following settings, say which inference procedure from Chapters $8, 9, 10, or 11$ you would use. Be specific. For example, you might say “two-sample z test for the difference between two proportions.” You do not need 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.

Step-by-Step Solution

Answer

a). The inference procedure of the chi-square independence test must be used for this setting.

b). The inference procedure of a two-sample independent t-test must be used for this setting.

Part (a) Step 1: Given Information

A random sample of $1000$ adults was asked whether they regularly attend religious services and whether they drink alcohol daily.

Part (a) Step 2: Explanation

A statistical test is to be conducted for determining whether there is a relationship between the variables attendance at religious services and alcohol consumption.

The variables considered in the setting are categorical variables because the response for variable 'attendance at religious services' would be 'present, absent' and the response for variable 'alcohol consumption' would be 'Yes, No'. The relationship between two categorical variables taken from the same population can be tested using the chi-square independence test.

Part (b) Step 1: Given Information

Separate random samples of $75$ college students and $75$ high school students were asked how much time, on average; Each week, they spend time watching TV. We're trying to figure out how much difference there is between high school and college students in terms of how much television they watch on average.

Part (b) Step 2: Explanation

To determine the difference in the average amount of TV viewed by high school and college students, a statistical test will be undertaken.

Two separate random samples of $75$ college students and $75$ high school students are taken. The two samples are clearly separate. There is also no indication that the two populations' standard deviations are known. The two-sample independent method is used since the population standard deviations are unknown and the samples are independent$t$ test must be used.