Does the percentage of women living at the home of a parent differ from the percentage of men living at the home of a parent? The NIH surveyed nm = 2253 random men and 2629 random women. Of these, xm = 986 of the men lived at the home of a parent and nf = 923 of the women lived at the home of a parent. Suppose pm is the true proportion of men living at the home of a parent. Suppose pf is the true proportion of women living at the home of a parent. pm and pf are unknown and we will examine relations between them based upon these samples. Let pmhat be the sample proportion of selected men living at the home of a parent. Let pfhat be the sample proportion of selected women living at the home of a parent.
(a) Calculate an unbiased point estimate of pm
(b) We wish to construct a 96% classical confidence interval for pm. What is the critical value multiplier zstar?
(c) Create a 96% classical confidence interval for pm
(d) How long is the 96% classical confidence interval for pm?
(e) In terms of pm = p and nm = n, give the formula for the standard deviation of the distribution of the sample proportion pmhat (R code)
(f) Calculate an unbiased point estimate of pf
(g) Calculate an unbiased point estimate of pm - pf
(h) Based on this data, calculate a 96% classical confidence interval for pm - pf
(I) How long is the 96% classical confidence interval for pm - pf calculated above?
(j) Write out R script or any other comments for the above