Assignment:
Q1. Two avid sports fans engage in an argument related to the difference in the batting averages of baseball teams of the American and National Leagues. To help settle the argument, perform a one-tail hypothesis using the information below to determine if the batting averages in the American League are higher than those of the National League.
American League National League
Mean batting averages .262 .251
Standard deviations .0125 .0114
Sample size 14 12
Q2. A large textbook publisher is concerned about the sale of complimentary desk copies of textbooks to wholesale book buyers. The publisher randomly samples the faculty from tow universities, A and B. Information provided by salespeople suggest that the faculty at University A had copies of the publisher's books which had been shipped, whereas the faculty at University B seldom had them.
A B
Sample size 150 120
Number of faculty who
Sold this publisher's book 75 78
At the .05 significance level, is this publisher reasonably justified in saying there is a higher proportion of faculty at University B who sell this publisher's complimentary books than at University A?
Q3. A state agency is debating whether or not to ask the Transportation Department to issue an order for a car manufacturer to recall certain models of a car which seem to be accelerating when the gear lever is shifted out of 'park'. Information needed is the proportion of drivers of this care who have had the problem of sudden acceleration. In order to estimate the proportion, a random sample of 500 owners of the car is taken. The manufacturer says the problem only happens in 1 out of 2000 cares or .0005. A 90% confidence interval is to be prepared. In the sample three of the five hundred reported having a sudden acceleration problem when shifting out of park. Compute the confidence interval and comment on the statement of the manufacturer.
Q4. A consumer research organization is attempting to determine whether there is any difference in MPG for fully loaded 22-foot trucks leased from three companies. A-Haul, Bertz, and Glyder. Five of these trucks are rented from each company. Each truck is driven with the same weight cargo over the same 200 miles route and the MPG recorded. The results of the test are:
A-Haul Bertz Glyder
3.4 5.1 7.9
4.2 2.0 8.5
5.1 8.7 5.2
4.9 6.7 8.0
3.1 6.1 8.1
A significance level of .05 is used by the consumer research organization. Is there any difference in mean MPG?
Q5. One of the most difficult industries in which to maintain long-term profit is the restaurant business. In an effort to stay abreast of changes in food preferences, a restaurateur compiles a list of menu orders. In the past, he has found the following percentages in menu choices: 2001
Mexican food 14%
Seafood 12%
Steak 30%
Hamburgers 8%
Italian entrees 10%
Chinese entrees 5%
Other 21%
In a sample of 300 orders, he observes the following. Using an appropriate statistical analysis, determine whether the pattern of menu selection has changed (assume a level of confidence of .05).
2002
Mexican food 54
Seafood 48
Steak 45
Hamburgers 30
Italian entrees 36
Chinese entrees 21
Other 66