MATHEMATICS

A social scientist believes that university theology professors are more conservative in political orientation than their colleagues in psychology. A random sample of 8 professors from the theology department and 12 professors from the psychology department at a local university are given a 50-point questionnaire that measures the degree of political conservatism. The following scores were obtained. Higher scores indicate greater conservatism.

a. What is the alternative hypothesis? In this case, assume a non-directional hypothesis is appropriate because there are insufficient theoretical and empirical bases to warrant a directional hypothesis.
b. What is the null hypothesis?
c. What is your conclusion? Use the Mann–Whitney U test and α = 0.052 tail.

Theology
Professors Psychology Professors
36 13
42 25
22 40
48 29
31 10
35 26
47 43
38 17
12
32
27
32

1. A psychologist investigates the hypothesis that birth order affects assertiveness. Her subjects are 20 young adults between 20 and 25 years of age. There are seven first-born, six second-born, and seven third born subjects. Each subject is given an assertiveness test, with the following results. High scores indicate greater assertiveness. Assume the data are so far from normally distributed that the F test can’t be used, but the data are at least of ordinal scaling. Use α =  0.01 to evaluate the data. What is your conclusion?

 

 

 

Condition 1

First-Born

Rank Condition 2

Second-Born

Rank Condition 3

Third-Born

Rank
18   18   7  
8   12   19  
4   3   2  
21   24   30  
28   22   18  
32   1   5  
10       14  
 

 = 7

 

 =

 

 = 6

 

 =

 

 = 7

 

 =

 

 

 

 

 

2. A major oil company conducts an experiment to assess whether a fi lm designed to tell the truth about, and also promote more favorable attitudes toward, large oil companies really does result in more favorable attitudes. Twelve individuals are run in a replicated measures design. In the “Before” condition, each subject fills out a questionnaire designed to assess attitudes toward large oil companies. In the “After” condition, the subjects see the film, after which they fi ll out the questionnaire. The following scores were obtained. High scores indicate more favorable attitudes toward large oil companies. Analyze the data using the Wilcoxon signed ranks

 

test with α = 0.05 (1 tail). What do you conclude?

 

 

 

 

 

Before After Difference Rank of (Difference) Signed Rank of Difference Sum of Positive Ranks Sum of Negative Ranks
43 45          
48 60          
25 22          
24 33          
15 7          
18 22          
35 41          
28 21          
41 55          
28 33          
34 44          
12 23          

 

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