AQ077-3-2-PSMOD Hypothesis Testing
1. A representative of a community group informs the prospective developer of a
shopping center that the average income per household in the area is $25,000.
Suppose that for the type of area involved household income can be assumed to be
approximately normally distributed and that the standard deviation can be accepted as
being equal to 2,000, based on an earlier study. For a random sample of n = 15
household, the mean household income is found to be
x
= $24,000.
(a) Test the null hypothesis that Āµ = $25,000 by establishing critical limits of
the sample mean in terms of dollars, using the 5 percent level of significance.
(b) Test the hypothesis by using the standard normal variable z as the test statistic.
2. The standard deviation of the tube life for a particular brand of ultraviolet tube is
known to be 500 hr, and the operating life of the tubes is normally distributed. The
manufacturer claims that average tube life is at least 9,000 hr. Test this claim at the 5
percent level of significance by designating it as the null hypothesis and given that for
a sample of n = 15 tubes the mean operating life was
x
= 8,800 hr.
3. For a sample of 50 firms taken from a particular industry the mean number of
employees per firm is 420.4 with a sample standard deviation of 55.7. There are a
total of 380 firms in this industry. Before the data were collected, it was hypothesized
that the mean number of employees per firm in this industry does not exceed 408
employees. Test this hypothesis at the 5 percent level of significance.
4. As a commercial buyer for a private supermarket brand, suppose that a random
sample of 12 No. 303 cans of string beans at a canning plant. The average weight of
the drained beans in each can is found to be
x
= 15.97 g, with s = 0.15. The claimed
minimum average net weight of the drained beans per can is 16.0 g. Can this claim be
rejected at the 10 percent level of significance?
5. An automatic soft ice cream dispenser has been set to dispense 4.00 g per serving. For
a sample of n = 10 servings, the average amount of ice cream is
x
= 4.05 g with
standard deviation = 0.10 g. The amount being dispensed are assumed to be normally
distributed. Basing the null hypothesis on the assumption that the process is āin
controlā, should the dispenser be reset as a result of a test at the 10 percent level of
significance?
6. It is hypothesized that no more than 5 percent of the parts being produced in a
manufacturing process are defective. For a random sample of n = 100 parts, 10 are
found to be defective. Test the null hypothesis at the 5 % level of significance.
7. A salesman claims that on the average he obtains orders from at least 30 percent of his
prospects. From a random sample of 100 prospects he is able to obtain 20 orders. Can
his claim be rejected at the (a) 5 % and (b) 1 % level of significance?
8. The sponsor of a television āspecialā expected that at least 40 percent of the viewing
audience would watch the show in a particular metropolitan area. For a random
sample of 100 households with television sets turned on, 30 are viewing the āspecialā.
Can the sponsorās assumption that at least 40 percent of the households would watch
the program be rejected at the (a) 10 percent and (b) 5 percent level of significance?
Level 2 Asia Pacific University of Technology and Innovation Page 1 of 3
