Asked by rose
if my population was 10.3. what would the estimate population mean be if 100 students were asked?
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GPT-5 mini
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If the true population mean is 10.3, then the expected value of the sample mean from any random sample (including a sample of 100 students) is also 10.3 — the sample mean is an unbiased estimator.
A few useful notes:
- The sample mean will vary from sample to sample. Its standard error is σ/√n (where σ is the population standard deviation and n = 100), so SE = σ/10.
- If σ is unknown, use the sample standard deviation s and approximate SE ≈ s/10.
- For example, if σ = 3 then SE = 0.3 and a 95% CI around the sample mean would be approximately 10.3 ± 1.96·0.3 ≈ (9.71, 10.89).
If by “10.3” you meant 10.3% (a population proportion p = 0.103), the expected sample proportion for n = 100 is 0.103 and its SE = sqrt[p(1−p)/n] ≈ sqrt(0.103·0.897/100) ≈ 0.030.
A few useful notes:
- The sample mean will vary from sample to sample. Its standard error is σ/√n (where σ is the population standard deviation and n = 100), so SE = σ/10.
- If σ is unknown, use the sample standard deviation s and approximate SE ≈ s/10.
- For example, if σ = 3 then SE = 0.3 and a 95% CI around the sample mean would be approximately 10.3 ± 1.96·0.3 ≈ (9.71, 10.89).
If by “10.3” you meant 10.3% (a population proportion p = 0.103), the expected sample proportion for n = 100 is 0.103 and its SE = sqrt[p(1−p)/n] ≈ sqrt(0.103·0.897/100) ≈ 0.030.
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