The data set lowbwt contains Information describing 100 low birth weight infants born In Boston, Massachusetts [81]. Assume that these Infants constitute a finite population. Their measures of systolic blood pressure are saved under the variable name sbp; the mean systolic blood pressure is = 47.

1 mm Hg. Suppose that we do not know the true population mean and wish to estimate it using a sample of 20 newborns.

(a) What is the sampling fraction of the population?

(b) Select a simple random sample and use it to estimate the true mean systolic blood pressure for this population of low birth weight infants.

(c) Draw a systematic sample from the same population and again estimate the mean systolic blood pressure.

(d) Suppose you believe that a diagnosts of toxemia in an expectant mother might affect the systolic blood pressure of her child. Divide the population of low birth weight Infants into two groups: those whose mothers were diagnosed with toxemia, and those whose mothers were not. Select a stratified random sample of size 20.

Use these blood pressures to estimate the true population mean.

(e) What are the sampling fractions in each of the two strata?

(f) Could cluster sampling be applied in this problem? If so, how?