Q. 74 - The Practice of Statistics for AP

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 want to estimate the average age at which U.S. presidents have died. So we obtain a list of all U.S. presidents who have died and their ages at death. 

(b) How much time do students spend on the Internet? We collect data from the $32$ members of our AP Statistics class and calculate the mean amount of time that each student spent on the Internet yesterday.

(c) Judy is interested in the reading level of a medical journal. She records the length of a random sample of $100$ words from a multipage article. The Minitab histogram below displays the data.

Step-by-Step Solution

Answer

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

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

(c) We can use $t$-procedure.

Part(a) Step 1: Given Information

Part(a) Step 2: Explanation

The sample contains the entire population, thus we can calculate the population mean directly and this means that it is not necessary to use the $t$-procedure.

Part(b) Step 1: Given Information

Part (b) Step 2: Explanation

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

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

Part(c) Step 1: Given Information

Part(c) Step 2: Explanation

There are $3$ requirements to use the $t$-procedure: Random, Independent, Normal

Random: The sample is given to be a random sample

Independent: Can be assumed, because the sample size of $100$ is less than $10\%$ of the population size.

Normal: Can be assumed, because the sample size of $100$ is larger than $30$.