For each of the following exercises, identify which of the following tests is the correct choice and state whether the test in one- or two-tailed. Explain your reasoning.
a) one-sample z test of proportions
b) two-sample z test of proportions
c) one-sample t test of means.
d) two-sample (independent) t test of means.
e) one-sample/two measurement (dependent) t test of means.
34) A recent article in Vitality magazine reported that the mean amount of leisure time per week for American men is 40.0 hours. You believe this figure is too large and decide to conduct your own test. In a random sample of 60 men, you find that the mean is 37.8 hours of leisure per week and that the standard deviation of the sample is 12.2 hours. Can you conclude that the information in the article is untrue? Use the .05 significance level. Determine the p-value and explain its meaning.
40) From past experience a television manufacturer found that 10 percent or less of its sets needed any type of repair in the first two years of operation. In a sample of 50 sets manufactured two years ago, 9 needed repair. At the .05 significance level, has the percent of sets needing repair increased? Determine the p-value.
24) Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the afternoon shift than on the day shift. A sample of 54 day-shift workers showed that the mean number of units produced was 345, with a standard deviation of 21. A sample of 60 afternoon-shift workers showed that the mean number of units produced was 351, with a standard deviation of 28 units. At the .05 significance level, is the number of units produced on the afternoon shift larger?
38) Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America's Cup race. They race over a part of the course several times. Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?
Prada12.9 12.5 11.0 13.3 11.2 11.4 11.0 12.3 14.2 11.3
Oracle 14.1 14.1 14.2 17.4 15.8 16.7 16.1 13.3 13.4 13.6 10.8 19.0
40) A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and the lights at those intersections were modified. The numbers of minor accidents during a six-month period before and after the modification were:
Number of Accidents
A B C D E F G H
Before modification 5 7 6 4 8 9 8 10
After modification 3 7 7 0 4 6 8 2
At the .01 significance level is it reasonable to conclude that the modification reduced the number of traffic accidents.
----Therefore, the above exercises don't need to be solved but just to figure out which test is correct, whether it's one or two-tailed, and the reasoning behind the answers.
This solution contains clear explanations on which t-test is appropriate in each scenario.