STATISTICS 3N03
TEST #3 * 2002-11-25
Instructions
Aids permitted: any calculators, any tables and one sheet of notes (8.5" x 11", one side only).
Questions
(b) What is a pivotal quantity? In general, how do you derive a test statistic from a pivotal quantity? In general, how do you derive a confidence interval from a pivotal quantity? [4 marks]
(b) If x is a vector of observations, what does the following R code compute? [4 marks]
> mu0 <- 27 > 2*(1-pt(abs((mean(x)-mu0)/sqrt(var(x)/length(x))),length(x)-1))
(a) A fleet manager is testing two brands of tires. He randomly assigns pairs of tires, one of each brand, to the front wheels of 8 cars, randomly deciding which brand goes on the left or right wheel in each case, and runs the cars until the tires wear out. The results are shown below, in thousands of km.
Car: 1 2 3 4 5 6 7 8 Brand A: 36.9 45.3 36.2 32.1 37.2 48.4 38.2 33.5 Brand B: 34.3 42.3 35.5 30.0 38.0 47.8 37.8 31.2
(b) The deflection temperature under load for two different types of plastic pipe is being investigated. Two random samples of 10 pipe specimens were tested. The observed deflection temperatures are tabulated below, in degrees Fahrenheit.
Type 1: 206 188 205 187 194 193 207 185 189 213 Type 2: 177 197 206 201 180 176 185 200 197 192