In a pilot study of the effect of dietary calcium on blood pressure, researchers measured the seated systolic blood pressure of 26 healthy adult males. The reported descriptive statistics werex= 116.9 mm Hg ands= 9.2 mm Hg (mm Hg = millimetres of mercury).

1. What conditions for the population measurements, sample data and sampling process are required for inferences about the population mean based on these statistics?
2. Of the conditions in part (a), which will be more important - those concerning the population measurements or those concerning the sampling process? Give reasons.
3. Assuming the relevant conditions are met, calculate a 95% confidence interval for the mean seated systolic blood pressure in the population from which the sample was selected.
4. Following the pilot study, a better estimate of the population mean is required. Specifically, we want to be 99% sure that the estimation error will be no more than 2 mm Hg. How large will the full-size random sample need to be?