ECO391 Homework Set 5 over Chapter 11 Hypothesis Testing
Spring 2003, Due on Wednesday, February 5, 2003, (worth 35 points)
1) A quality control inspector tests the dimensions of parts used in a machining operation.
Specifications require that the mean diameter of the parts be 2 inches. If a sample leads the
quality control inspector to believe that the diameters are too large or too small, the machine is
shut down and readjusted. State the appropriate null and alternative hypotheses for
determining whether the machine should be shut down. (2 points)
2) An experiment is carried out to determine whether a new anesthetic results in lower death
rates than other anesthetics. (2 points each part)
a) What should the null hypothesis be? What should the alternative hypothesis be?
b) Describe a type I error in this scenario and the anticipated medical consequences.
c) Describe a type II error in this scenario and the anticipated medical consequences.
3) A tire manufacturer claims that its tires have a mean life of at least 35,000 miles. Some
unhappy consumers have argued otherwise. A random sample of 16 of these tires is tested and
the sample mean is 33,000 miles. Assume the population standard deviation is 3,000 and the
lives of tires are approximately normally distributed. Test the claim of the unhappy customers
using a 5% level of significance. (6 points)
4) A random sample of 100 observations from a normal population produced a sample mean of
231.7 and a sample standard deviation of 9.3. (The true population standard deviation is
unknown.) At the 1% level of significance, test to see whether or not the true population
average is equal to 225. (6 points)
5) There are a variety of government agencies devoted to ensuring that food producers package
their products in such a way that the weight or volume of the contents listed on the label is
correct. For example, bottles of catsup whose labels state that the contents have a net weight
of 16 ounces, must have a net weight of at least 16 ounces. However, it is impossible to check
all packages sold in the country. As a result, statistical techniques are used. A random sample
of the product is selected and its contents measured. If the mean of the sample provides
sufficient evidence to infer that the mean weight of all bottles is less than 16 ounces, the
product label is deemed to be unacceptable. Suppose that a government inspector weighs the
contents of a random sample of 25 bottles of catsup labeled "new weight: 16 ounces" and
records the measurements (see below.) Using a 10% level of significance, can the product
inspector conclude that the product label is unacceptable? (9 points)
Net Weight of "16 ounce" catsup bottles:
15.8 16.0 16.2 15.7 15.4 16.1
16.2
16.2 15.6 16.0 16.8 15.7 15.6 15.3
17.3
15.7
15.0
15.8
16.8
15.6
15.6
15.5
15.9
15.7
16.0
6) A magazine claims that at least 25% of its subscribers are college graduates. In a random
sample of 200 subscribers, 41 are college graduates. Use a 5% level of significance to test the
validity of the magazine's claim. (6 points)