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 were x = 118.9 mm Hg and s = 8.8 mm Hg (mm Hg = millimetres of mercury). (a) What conditions for the population measurements, sample data and sampling process are required for inferences about the population mean based on these statistics? [3] (b) Of the conditions in part (a), which will be more important - those concerning the population measurements or those concerning the sampling process? Give reasons. [2] (c) 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. [3] (d) 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?