Question

if my population was 10.3. what would the estimate be if 100 students were asked?

Answer 1

I’m not certain what you mean by “population was 10.3” — do you mean a population mean of 10.3, or a population proportion of 10.3% (0.103)? I’ll give both interpretations:

1) If 10.3 is the population mean (μ = 10.3)
- The expected sample mean from 100 students is the same: 10.3 (the sample mean is an unbiased estimator of the population mean).
- The standard error of the sample mean = σ / sqrt(n) = σ / 10. You need the population (or sample) standard deviation σ to compute a numeric SE and any confidence interval.

2) If 10.3 means 10.3% (p = 0.103), i.e. a population proportion
- The expected number of students (out of 100) with the trait ≈ 100 × 0.103 = 10.3 (about 10 students).
- The sample proportion p̂ is an unbiased estimator and its standard error = sqrt[p(1−p)/n] = sqrt(0.103×0.897/100) ≈ 0.0304 (≈ 3.04 percentage points).
- A 95% CI for the proportion ≈ 0.103 ± 1.96×0.0304 ≈ (0.043, 0.163) or about 4.3% to 16.3%.

Tell me which interpretation you intended (mean or percent) and, if it’s the mean, give a standard deviation (or sample SD) if you want the numerical SE or confidence interval.