Hypothesis Testing

11. 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

12. 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?

13. 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.

14. 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?

15. 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