* do-file for Supplementary Exercises 6.38 and 6.39 of IPS7e
version 17 /* works also with version 16 */

* using either the command or the Power and sample size menu (Confidence interval)
* the ciwidth command was introduced with Stata 16

* 6.38
* for known population standard deviation
ciwidth onemean, width(800) sd(9000) knownsd

* for unknown and hence estimated standard deviation
ciwidth onemean, probwidth(.5) width(800) sd(9000)
ciwidth onemean, probwidth(.8) width(800) sd(9000)

* note on Stata implementation with estimated standard deviation:
Stata additionally requires specification of the "probability of
achieving target CI width" (probwidth option). This is similar to the
probability set for the power in sample size calculations based on
power. Setting the value around 0.5 will give results similar to those
obtained with t*-values instead of z*-values. This adjusts for the use
of the estimated standard deviation in the calculation of the CI, but
does not adjust for the variation in the estimated standard deviation:
the sample estimates will not be equal to the stated value for standard
deviation, and hence the actual confidence intervals will be either larger
or smaller than the specified margin of error. Therefore, setting this
probability at a reasonably high value (e.g. 0.8 or 0.9) will make it
more likely that the CI achieves its target, but (naturally) at the cost
of a larger sample size.

* 6.39
* for known population standard deviation
ciwidth onemean, width(1600) sd(9000) knownsd
* for unknown and hence estimated standard deviation
ciwidth onemean, probwidth(.5) width(1600) sd(9000)
ciwidth onemean, probwidth(.8) width(1600) sd(9000)