Q.59 - 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 Chapter $8, 9, 10, or 11$ 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) 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 actually 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.

Step-by-Step Solution

Answer

a). The $Z$ test used when SD is known and the $T$ test is used when SD is unknown.

b). The difference between two proportions is given by two-sample $Z$ test.

Part (a) Step 1: Given Information

A random sample of $38$ cities was asked to report the percent of registered voters who actually voted in the most recent election.

Part (a) Step 2: Explanation

During an election, perform the following test to determine the average voter turnout:

The average voter turnout during an election is of particular importance to the investigator.

The researcher took a random sample of $38$ cities and calculated the percentage of registered voters who voted in the most recent election.

When the population standard deviation is known, the sample $Z$-test for the single mean is applied.

The population standard deviation is unknown because just one sample of $T$-test for a single mean is employed.

Part (b) Step 1: Given Information

The Independent random samples of $300$ blondes and $300$ non blondes were asked whether they have a boyfriend.

Part (b) Step 2: Explanation

To see if blondes are more likely than the rest of the single world to have a boyfriend, do the following: The researcher is particularly interested in seeing if blondes are more likely than the rest of the single world to have a boyfriend.

The researcher chose two separate random samples of $300$ blondes and $300$ nonblondes and asked them if they had a boyfriend or not.

Since the samples are large, then we take $z-test$.