It would also be appropriate to report this result as mean ± 95% CI

Question

BlackTom AI · Accepted Answer

A mean reported with a 95% confidence interval presents both the point estimate and its precision: mean ± (critical value) × standard error. This is a standard and appropriate way to report a sample mean when the sampling distribution of the mean is approximately normal (either because the population is normal or because the sample size is large and the Central Limit Theorem applies).

1) Relevant knowledge points and concepts
- Point estimate: the sample mean x̄.
- Standard error (SE): s/√n, where s is the sample standard deviation and n the sample size.
- 95% confidence interval (CI): x̄ ± tα/2,df × SE (use z≈1.96 for large n, use t with df = n−1 for small n).
- CI expresses uncertainty about the population mean; it is not the same as mean ± SD (which describes variability of individual observations).

2) Step-by-step reasoning
- Compute the sample mean x̄.
- Compute sample standard deviation s and then SE = s/√n.
- Choose the critical value: t0.975,n−1 (or z = 1.96 for large n).
- Multiply the critical value by SE to get the margin of error.
- Report the CI as x̄ ± margin of error (or equivalently as (lower bound, upper bound)).

3) Calculation template (intermediate steps)
- SE = s / √n
- margin of error = t0.975,n−1 × SE
- 95% CI = x̄ ± margin of error

4) Why the correct answer is correct
Reporting mean ± 95% CI directly communicates the estimated population mean and the interval in which we are 95% confident the true mean lies, given the data and assumptions. It is a conventional and informative way to present results for normally distributed (or large-sample) continuous data.

5) Why the other option (False) is incorrect
Saying it would not be appropriate (False) would ignore that mean ± 95% CI is a standard, informative summary. The only caveat is when data are highly skewed or contain outliers—in such cases median and IQR might be preferable—but that doesn’t make the mean±95%CI generally inappropriate.

6) Conclusion
Therefore, it is appropriate to report the result as mean ± 95% CI. This matches the provided answer: True.

It would also be appropriate to report this result as mean ± 95% CI判断题

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