Chapter 11
Many drivers of cars that can run on regular gas actually buy premium in the belief that they will get better gas mileage. To test that belief, 10 cars in a company fleet were randomly selected. All the cars run on regular gas. Each car was filled first with either regular or premium gasoline, decided by a coin toss. The mileage for that tank of gas was recorded. Then the car was filled with the other type of gasoline and the mileage for that tank of gas was recorded. The summary statistics for the difference in gas mileage between the two types of gasoline (premium−regular) for the 10 cars are x=2 and s=1.414. Suppose the p-value was 0.001. Which of the following is the correct conclusion?
There is sufficient evidence to indicate that the gas mileage using premium gasoline is better than using regular gasoline, on average. With a small p-value, there is evidence to reject the null hypothesis, which is that the average of the differences in gas mileage between premium and regular gasoline is 0.
A certain marathon has had a wheelchair division since 1977. An interested fan wondered who is faster: the men's marathon winner or the women's wheelchair marathon winner, on average. A paired t-test was performed, and the p-value was found to be 0.001. Which of the following is the correct conclusion?
There is sufficient evidence to indicate that the men's running winning time and the women's wheelchair winning time each year are different, on average.
In 1993, the British Medical Journal published an article titled, "Is Friday the 13th Bad for Your Health?" Researchers in Britain examined how Friday the 13th affects human behavior. One question was whether people tend to stay at home more on Friday the 13th. The accompanying data give the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays (the 6th and 13th) for five different time periods. Assuming all conditions for inference are met, which test is appropriate to use to answer the researcher's question of interest?
paired t-test
Some students do homework with the TV on. Researchers wanted to see if people can work as effectively with distractions as without them. From a group of student volunteers, researchers randomly assigned half to do a relatively easy crossword puzzle in a quiet room and the other half to do the same crossword puzzle in a room in which a TV was on. Then each volunteer was to do a different relatively easy crossword puzzle under the other condition. Students were timed on how long it took to complete the puzzle and the difference in each student's quiet-room time and TV-room time was recorded. Which test is appropriate to use to determine if students take longer to complete the puzzle in the TV room compared to the quiet room, on average?
paired t-test because an observation in the quiet-room group was directly associated with a particular observation in the TV group—each person was in both groups.
