In a study of dyslipidemia, a sample of 18 male participants was drawn from male adult population and a sample of 36 female participants was drawn from female adult population to measure their low-density lipoprotein (LDL) cholesterol level in their blood. The study results found 4 participants in the male sample had high LDL level (i.e., LDL level was ≥ 100 mg/dL); and 9 participants in the female sample had high LDL.
a) It is postulated that 30% of male adults have high LDL in the male adult population. If this hypothesis is true, what is the probability of observing 4 or less male participants with a high LDL in a male adult sample of size 18?
b) At the 0.05 level of significance, test the null hypothesis (state H0, HA, critical value, and pvalue) that the proportions of high LDL are equal among male and female populations.
c) Construct a 95% confidence interval for the true difference in population proportions of high LDL (p1-p2) between female and male populations.