From Koosis, I pieced together the following algorithm.(adsbygoogle = window.adsbygoogle || []).push({});

Is sigma known?

Yes? Then calculate the exact confidence interval using a normal distribution to estimate that of the sample means, with mean = the mean of sample means = the mean of the population, [itex]\mu_{\overline{x}}=\mu[/itex], and standard deviation [itex]\sigma_{\overline{x}}=\sigma/\sqrt{n}[/itex].

No? Then is the poplation normal?

Yes? Then (a) estimate the confidence interval with a Student's t distribution for the sample means, using degrees of freedom dof = n - 1, and standard deviation [itex]s_{\overline{x}}=s\sqrt{n}[/itex], or (b) for a slightly inferior result, and only if [itex]n\geq 30[/itex], estimate the confidence interval using the normal distribution with mean [itex]\mu_{\overline{x}}=\mu[/itex], and standard deviation [itex]s_{\overline{x}}=s\sqrt{n}[/itex].

No or don't know? Then is [itex]n\geq 30[/itex]?

Yes? Then estimate the confidence interval, using a normal distribution to estimate that of the sample means, with mean [itex]\mu_{\overline{x}}=\mu[/itex], and standard deviation [itex]s_{\overline{x}}=s\sqrt{n}[/itex].

No? Then can't do.

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But Sanders has the following, somewhat different algorithm.

Is [itex]n\geq 30[/itex]?

Yes? Then use z values in computations.

No? Then are population values known to be normally distributed?

Yes? If the population standard deviation of the population is known, use z values in computations. Otherwise, use t values in computations.

No? Cannot use z or t values in computations.

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Any comments on which is the best procedure? Actually Koosis presented the z test first, as if he, like Sanders, assumed that one would choose this over the t test wherever possible, even though he said it wasn't as good when both choices were possible. I wonder why z beats t in that case? Is it because the difference in accuracy is negligible then and the computations for t potentially more time consuming than those for z? (And if so, is this still the case with current software; both books are a few years old.)

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# Finding or estimating confidence interval for populaion mean

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