Chapter 9

1.   Last year the labor union bargaining agents listed 5 items and asked each employee to mark the one most important to him or her.  The items and corresponding percentage of favorable responses is given below.  The bargaining agents need to know if the distribution of responses now “fits” last year’s distribution or is it different.  A new survey is taken and the results of 500 employee responses are listed under This Year.  Test using .

Bargaining Items	% Favorable(last year)	This Year
Vacation Time	4%	30
Salary	65%	290
Safety Regulations	13%	70
Health/Retirement	12%	70
Overtime Policy/Pay	6%	40

 

2.     A particular state university system has 6 campuses.  On each campus, a random sample of students will be selected, and each student will be categorized with respect to political philosophy as liberal, moderate, or conservative.  The null hypothesis of interest is that the proportion of students falling in these three categories is the same at all 6 campuses.
A. On how many degrees of freedom will the resulting  test be based?
B. How does your answer in part a change if there are seven campuses rather than 6?
C. How does your answer in part a change if there are four rather than 3 categories for political philosophy?

3.     A random sample of 1000 registered voters in a certain county is selected, and each voter is categorized   with respect to both educational level (four categories) and preferred candidate in an upcoming election (five possibilities).  The hypothesis of interest is that educational level and preferred candidate are independent factors.
A. If   = 7.2, what would you conclude at significance level 0.10?
B.  If there were only four candidates vying for election, what would you conclude if  = 14.5 and ?

 

4.    Suppose that we were to poll homeowners about their feeling on a governor’s proposal to lower property taxes.  In a poll, 200 urban, 200 suburban and 100 rural residents were randomly selected and asked whether they favor or oppose the governor’s proposal.  Thus, a total of 500 people were sampled, but it is predetermined (before the sample is taken) just how many are to fall within each category.  Does the sample evidence support the hypothesis that “voters within the different residence groups have different opinions about the tax proposal”?

Type of Residence	Favor	Oppose	Total
Urban	143	57	200
Suburban	98	102	200
Rural	13	87	100
Total	254	246	500

 

5.    Until recently a number of professions were prohibited from advertising.  In 1977, the U.S. Supreme Court ruled that prohibiting doctors and lawyers from advertising violated their right to free speech.  The paper “Should Dentists Advertise?”  (Journal of Advertising Research  (June, 1982)) compared the attitudes of 101 consumers and 124 dentists to the question “I favor the use of advertising by dentists to attract new patients”.  The authors were interested in determining whether the two groups differed in their attitudes toward advertising.  A significance test of 0.05 was used.

Group	Strongly Agree	Agree	Neutral	Disagree	Strongly Disagree	Row Marginal Total
Consumers	34	47	9	6	5
Dentists	9	18	23	28	46
Column Marginal Total