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. How much time do students at your school spend on the Internet? You collect data from the $32$members of your AP Statistics class and calculate the mean amount of time that these students spent on the Internet yesterday.

b. Is the real-estate market heating up? To estimate the mean sales price, a realtor in a large city randomly selected $100$home sales from the previous $6$months in her city. These sales prices are displayed in the boxplot.

Short answer

a. Random Sample condition is not met.

b. All conditions are satisfied.

Step-by-step solution

Part (a) Step 1: Given Information

It is given that $n=32$

Population is of all students.

Part (a) Step 2: Explanation

Random: AP Statistics is chosen as per requirement. It can never be random sample.

Less than $10\%$of population: $32$students are less than $10\%$of students. This condition is not satisfied.

Sample Size: $32>30$, sample size is larger. Condition of large sample size is satisfied.

Condition of Random sample is not met.

Part (b) Step 1: Given Information

It is given that $n=100$

Population is of all home sales in city.

Part (b) Step 2: Explanation

Random: Home sales are to be selected randomly. Hence, this condition is satisfied.

Less than $10\%$ of population: $100<10\%$of all population. This is also satisfied.

Large Sample Size: $100>30$, this condition is also met.

All conditions are satisfied.