Chapter 8: Q 65. (page 542)

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.

Expert verified

a. Random Sample condition is not met.

b. All conditions are satisfied.

Step by step solution

It is given that $n = 32$

Population is of all students.

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.

It is given that $n = 100$

Population is of all home sales in city.

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.

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