STAT412 In-Class Exercise
Analysis of Categorical Data
1. A university library ordinarily has a complete shelf inventory done once
every year. Because of new shelving rules instituted the previous year, the
head librarian believes it may be possible to save money by postponing the
inventory. The librarian decides to select at random 1000 books from the
library’s collection and have them searched in a preliminary manner. If
evidence indicates strongly that the proportion of misshelved or unlocatable
books in the population is less than .02, then the inventory will be postponed.
Among the 1000 books searched, 15 were misshelved or unlocatable.
Conduct hypothesis test and advise the librarian what to do (use   .05. ).
2. Are the educational aspirations of students related to family income? This
question was investigated in the article “Aspirations and Expectations of
High School Youth” (Int. J. of Comp. Soc. (1975): 25). The accompanying 4
X 3 table resulted from classifying 273 students according to expected level
of education and family income. Does the data indicate that education
aspirations and family income are not independent? Conduct hypothesis test
using = .05.
Aspired Level
Some High School
High School Graduate
Some College
College Graduate
Low
9
44
13
10
Income
Middle
11
52
23
22
High
9
41
12
27
3. A statistics department at a state university maintains a tutoring service for
students in its introductory service courses. The service has been staffed
with the expectation that 40% of its students would be from the business
statistics course, 30% from engineering statistics, 20% from the statistics
course for social science students, and the other 10% from the course for
agriculture students. A random sample of n=120 students revealed 50, 40,
18, and 12 from the four courses. Does this data suggest that the percentages
on which staffing was based are not correct? Conduct hypothesis using
  .05.
4. A sample of 300 urban adult residents of in Michigan revealed 63 who
favored increasing the highway speed limit from 55 to 70mph, whereas a
sample of 180 rural residents yielded 72 who favored the increase. Does this
data indicate that the sentiment for increasing the speed limit is different for
the two groups of residents? Conduct hypothesis test using =.05.
5. A plan for an executive traveler’s club has been developed by an airline on
the premise that 5% of its current customers would qualify for membership.
A random sample of 500 customers will be selected and the researcher will
test the null hypothesis that the company’s premise is correct against the
alternative that it is not correct, using  = .01 What is the probability of
failing to reject H0 if in fact 10% of all current customers qualify?