Questions: Four scenarios of statistical studies are given below. Decide which study uses a population parameter. 15% of the attendees at a town council meeting in a rural area reported not using the internet on a daily basis. In the 1950s, Eugene Gilbert interviewed 3975 parents and found that 29% thought rock 'n' roll should be banned from their communities. The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time of 5:53, and an average run As. part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election. 39 said yes.

Four scenarios of statistical studies are given below. Decide which study uses a population parameter.

15% of the attendees at a town council meeting in a rural area reported not using the internet on a daily basis.
In the 1950s, Eugene Gilbert interviewed 3975 parents and found that 29% thought rock 'n' roll should be banned from their communities.
The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time of 5:53, and an average run As. part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election. 39 said yes.

Transcript text: Four scenarios of statistical studies are given below. Decide which study uses a population parameter. $15 \%$ of the attendees at a town council meeting in a rural area reported not using the internet on a daily basis. In the 1950s, Eugene Gilbert interviewed 3975 parents and found that $29 \%$ thought rock ' $n$ ' roll should be banned from their communities. The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time of 5:53, and an average run As. part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election. 39 said yes.

Solution

Solution Steps

To determine which study uses a population parameter, we need to identify if the data provided is based on the entire population or just a sample. A population parameter is a value that represents a characteristic of the entire population, whereas a sample statistic is derived from a subset of the population.

The first scenario mentions attendees at a town council meeting, which is likely a sample of the entire town's population.
The second scenario involves interviewing 3975 parents, which is a sample of all parents.
The third scenario provides average times for all 1883 finishers of the Ironman, Kona, which represents the entire population of finishers.
The fourth scenario involves asking 84 classmates, which is a sample of all classmates.

The third scenario uses a population parameter because it includes data from the entire population of finishers.

Step 1: Identify the Scenarios

We have four scenarios regarding statistical studies. Each scenario presents data that may either represent a sample or a population. The goal is to determine which scenario uses a population parameter.

Step 2: Analyze Each Scenario

Scenario 1: $ 15\% $ of the attendees at a town council meeting reported not using the internet daily. This is based on a sample of attendees, not the entire population of the town.
Scenario 2: In the 1950s, $ 29\% $ of $ 3975 $ interviewed parents thought rock 'n' roll should be banned. This is also a sample of parents, not the entire population.
Scenario 3: The average finish time for the Ironman, Kona was $ 11:32 $ for $ 1883 $ finishers. This data represents the entire population of finishers, making it a population parameter.
Scenario 4: Kaisa asked $ 84 $ classmates if they voted in the last presidential election, which is a sample of all classmates.

Step 3: Conclusion

The only scenario that uses a population parameter is the third one, which provides average times for all $ 1883 $ finishers of the Ironman, Kona.