Q. 73

Question

In each of the following situations, discuss whether it would be appropriate to construct a one-sample $t$ interval to estimate the population mean.

(a) We collect data from a random sample of adult residents in a state. Our goal is to estimate the overall percentage of adults in the state who are college graduates.

(b) The coach of a college men’s basketball team records the resting heart rates of the $15$ team members. We use these data to construct a confidence interval for the mean resting heart rate of all male students at this college.

(c) Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of $25$ randomly selected students. The Fathom boxplot below displays the difference (texts calls) for each student.

Step-by-Step Solution

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Answer

(a) The $z$ -procedure is used when estimating the population proportion. Therefore $t$ - procedure is not used.

(b) We do not use $t$ - procedure.

1Part(a) Step 1: Given Information

2Part(a) Step 2: Explanation

The overall percentage of adults is a population proportion.

The $t$ -procedure is used when estimating a population mean and not for the population proportion.

3Part(b) Step 1: Given Information

4Part(b) Step 2: Explanation

The sample is a convenience sample because the individuals were conveniently selected as the team members.

A convenience sample is NOT a random sample and thus the RANDOM requirement for the $t$ -procedure is not satisfied.

5Part(c) Step 1: Given Information

6Part(c) Step 2: Explanation

In the boxplot we note that there are $3$ outliers and the distribution appears to be right-skewed (since the line in the box of the boxplot is more to the left of the box).

Since the distribution contains outliers and skewness, the distribution is NOT approximately a normal distribution.

The NORMAL requirement to use the $t$ -procedure is thus not satisfied.

Q. 72

Q. 74

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