1. Tutorial 4
For the Seat Belt Data, the Death Penalty Data, and the University Admission Data,
(1). Identify the response variable and the explanatory variable, and construct 95% and 99% confidence intervals for each proportion p1 and p2.
(2). Construct the 95% and 99% CI for the difference between the two proportions.
(3). Test the hypothesis of independence against an “appropriate” alternative hypothesis.
(4). Estimate the odds-ratio, find its standard error and construct 95% and 99% CIs.
2. For the Vitamin C data and the Death Penalty data, compare the values of the three z-statistics based on the ordinary difference, the odds-ratio and the log-odds-ratio respectively for testing the hypothesis of independence. Do they lead to different conclusions?
(Direct computation of the z statistic for a 2x2 table) For a 2x2 table with entries a,b, c and d,
Response Group Group 2
Positive a b
Negative c d
Show that the ordinary z-statistic for testing independence (i.e the one based on the ordinary difference) may be written as
1/18/2019
SA3202, Tutorial 4