Asked by A
Here are the ages (in years) of a random sample of 10 students for 3 different
afterschool activities. The activities are sports activity, watch younger siblings, and
work.
Sample
1 12 12 11 10 8 9 9 11 12 9
Sample
2 16 15 16 16 17 15 16 17 17 15
Sample
3 12 13 14 15 14 13 12 16 17 15
1. Calculate the mean for one of the samples. Which activity do you think the
sample represents? Explain your reasoning.
2. Using the sample, estimate the population mean if 100 students were asked.
All Answers 1
Answered by
GPT-5 mini
AI
First I’ll compute the sample means (sum of ages ÷ 10):
- Sample 1: values = 12, 12, 11, 10, 8, 9, 9, 11, 12, 9
Sum = 103 → mean = 103/10 = 10.3 years
- Sample 2: values = 16, 15, 16, 16, 17, 15, 16, 17, 17, 15
Sum = 160 → mean = 160/10 = 16.0 years
- Sample 3: values = 12, 13, 14, 15, 14, 13, 12, 16, 17, 15
Sum = 141 → mean = 141/10 = 14.1 years
1) Which activity each sample likely represents:
- Sample 1 (mean 10.3): most likely the sports activity — ages are younger (8–12), typical of kids in after‑school sports.
- Sample 2 (mean 16.0): most likely work — ages are older (15–17), which fits teens who have jobs.
- Sample 3 (mean 14.1): most likely watching younger siblings — middle‑teen range, plausible for older children caring for siblings.
(Reason: I matched each sample by the typical ages one would expect for each activity: work requires older teens, sports often include younger children, and watching siblings tends to fall in between.)
2) Estimating the population mean if 100 students were asked:
- The best point estimate of the population mean is the sample mean (assuming the sample is representative). So the estimated population means would be:
- Sample 1 → 10.3 years
- Sample 2 → 16.0 years
- Sample 3 → 14.1 years
If you instead want the estimated total age for 100 students, multiply the mean by 100:
- Sample 1 total ≈ 10.3 × 100 = 1030 years
- Sample 2 total = 16.0 × 100 = 1600 years
- Sample 3 total ≈ 14.1 × 100 = 1410 years
Note: these estimates assume each 10‑student sample is representative of the 100 students.
- Sample 1: values = 12, 12, 11, 10, 8, 9, 9, 11, 12, 9
Sum = 103 → mean = 103/10 = 10.3 years
- Sample 2: values = 16, 15, 16, 16, 17, 15, 16, 17, 17, 15
Sum = 160 → mean = 160/10 = 16.0 years
- Sample 3: values = 12, 13, 14, 15, 14, 13, 12, 16, 17, 15
Sum = 141 → mean = 141/10 = 14.1 years
1) Which activity each sample likely represents:
- Sample 1 (mean 10.3): most likely the sports activity — ages are younger (8–12), typical of kids in after‑school sports.
- Sample 2 (mean 16.0): most likely work — ages are older (15–17), which fits teens who have jobs.
- Sample 3 (mean 14.1): most likely watching younger siblings — middle‑teen range, plausible for older children caring for siblings.
(Reason: I matched each sample by the typical ages one would expect for each activity: work requires older teens, sports often include younger children, and watching siblings tends to fall in between.)
2) Estimating the population mean if 100 students were asked:
- The best point estimate of the population mean is the sample mean (assuming the sample is representative). So the estimated population means would be:
- Sample 1 → 10.3 years
- Sample 2 → 16.0 years
- Sample 3 → 14.1 years
If you instead want the estimated total age for 100 students, multiply the mean by 100:
- Sample 1 total ≈ 10.3 × 100 = 1030 years
- Sample 2 total = 16.0 × 100 = 1600 years
- Sample 3 total ≈ 14.1 × 100 = 1410 years
Note: these estimates assume each 10‑student sample is representative of the 100 students.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.