Chapter 11: Q. 61 (page 759)

Inference recap ( $8.1$ to $11.2$ ) In each of the following settings, state which inference procedure from Chapter $8, 9, 10, o r 11$ 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. What is the average voter turnout during an election? A random sample of $38$ cities was asked to report the percent of registered voters who voted in the most recent election.
b. Are blondes more likely to have a boyfriend than the rest of the single world? Independent random samples of $300$ blondes and $300$ nonblondes were asked whether they have a boyfriend.

Short Answer

Expert verified

a. One-sample t interval for the mean should be used.

b. Z-test of proportion for two sample 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

Whenitcomestoelections,whatisthetypicalvoterturnout?

The percentage of registered voters who voted in the most recent election was requested from a random sample of

33

cities.

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. It is necessary to check the average voter in the given scenario.

That is to say, you are interested in the average of one sample. As a result, the mean should be calculated using a one-sample t interval.

Part (b) Step 1 : Given information

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

Part (b) Step 2 : Simplification

Are blondes more likely than the rest of the single world to have a boyfriend?

300

blondes and

300

nonblondes were randomly selected and asked if they had a boyfriend.

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. Check rises in the difference of two proportions of two samples in the provided example.

As a result, the proportion Z-test for two samples should be utilized.