Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 230■ Example 8.9: Differing dosages of AZTAZT was the first FDA-approved antiretroviral drug used in the care of HIVinfectedindividuals. The common dosage is 300 mg twice daily. Higher dosages cause more sideeffects. But are they more effective? A study done in 1990 compared dosages of 300 mg,600 mg, and 1,500 mg (source http://www.aids.org/). The study found higher toxicitywith greater dosages, and, more importantly, that the lower dosage may be equallyeffective.The p24 antigen can stimulate immune responses. The measurement of p24 levels forthe 300 mg and 600 mg groups is given by the simulated data in Table 8.4. Perform a t-test to determine whether there is a difference in means.Table 8.4 Levels of p24 in mg for two treatmentgroupsAmountp24 level300 mg 284 279 289 292 287 295 285 279 306 298600 mg 298 307 297 279 291 335 299 300 306 291Let µ x be the mean of the 300 mg group, and µ y the mean of the 600 mg group. We cantest the hypothesesH 0 :µ x =µ y , H A :µ x ≠µ ywith a t-test. First, we check to see whether the assumption of a common variance andnormality seems appropriate by looking at two densityplots:> x = c(284, 279, 289, 292, 287, 295, 285, 279, 306,298)> y = c(298, 307, 297, 279, 291, 335, 299, 300, 306,291)> plot(density(x))> lines(density(y), lty=2)The graph (Figure 8.5) shows two density estimates that indicate normally distributedpopulations with similar spreads. As such, the t-test looks appropriate.