Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 200We use the argument conf . level=… to specify the confidence level.■ Example 7.10: Comparing shoes The shoes (MASS) data set contains shoe wear forten children each wearing two different shoes. By comparing the differences, we can tellwhether the two types of shoes have different mean wear amounts.> library(MASS) # load data set> names(shoes)[1] "A" "B"> with(shoes, t.test(A-B,conf.level = 0.9))One Sample t-testdata: A − Bt = −3.349, df = 9, p-value = 0.008539alternative hypothesis: true mean is not equal to a90 percent confidence interval:−0.6344 −0.1856sample estimates:mean of x−0.41### Alternately:> with(shoes, t.test(A,B,conf.level = 0.9,paired=TRUE))...Both approaches produce the same 90% confidence interval. In this case, it does notinclude a, indicating that there may be a difference in the means.7.5.4 Problems7.25 Two different AIDS-treatment “cocktails” are compared. For each, the time it takes(in years) to fail is measured for seven randomly assigned patients. The data is in Table7.1. Find an 80% confidence interval for the difference of means. What assumptions areyou making on the data?Table 7.1 Time to fail for AIDS cocktails, inyearsType 1 2 3 4 5 6 7 sCocktail 1: 3.1 3.3 1.7 1.2 0.7 2.3 2.9 2.24 0.99Cocktail 2: 1.8 2.3 2.2 3.5 1.7 1.6 1.4 2.13 0.697.26 In determining the recommended dosage of AZT for AIDS patients, tests were donecomparing efficacy for various dosages. If a low dosage is effective, then that would berecommended, as it would be less expensive and would have fewer potential side effects.A test to decide whether a dosage of 1,200 mg is similar to one of 400 mg isperformed on two random samples of AIDS patients. A numeric measurement of apatient’s health is made, and the before-and-after differences are recorded after treatment