Question

Check them all Determine if the conditions are met for constructing a confidence interval for the population mean in each of the following settings.

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. 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 boxplot displays the difference (Texts − Calls) for each student.

Short answer

a. The conditions not met are: Random Sample and Independent.

b. Condition not met is of Large Sample.

Step-by-step solution

Part (a) Step 1: Given Information

It is given that population is taken of all US president.

Part (a) Step 2: Explanation

Conditions are:

• Random: In sample, all US president are included. It cannot be random sample.
• Independence: Sample of US presidents can never be less than $10\%$of total population of US president.
• Large Sample Size: It will be $>30$as they are for sure more than $30$

The conditions not met are: Random Sample and Independent.

Part (b) Step 1: Given Information

It is given that $n=25$

Population is of all the students.

Part (b) Step 2: Explanation

Conditions are:

• Random: This is satisfied as students are selected randomly.
• Independent: $25<10\%$of population of all students.
• Large Sample Size: $25<30$. This is not met.

Condition of Large Sample is not met.