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# Statistics (10 Problems) : Hypothesis Testing, Chi-Square, Nonparametric Tests and Mann-Whitney U Test

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2. A researcher randomly selects a sample of college students majoring in physics, chemistry, psychology, P.E., or English lit. He notes each student's major subject, and also whether that student is a blonde, a brunette, or a redhead. The data are as follows:

Physics Chem Psych P.E. English Total
Blonde 8 10 20 4 10 52
Brunette 10 8 30 3 10 61
Redhead 5 3 10 14 10 42
Totals 23 21 60 21 30 155

Can the researcher conclude that the relationship between major and hair color is greater than would be expected by chance alone?

3. You randomly selected 10 men and 10 women from a large college class, mixed up their names, and asked the professor to put them in order in terms of attentiveness. After some grumbling, the professor agreed; the next week, he arranged the names as follows (most attentive first):

1. Ann
2. Sue
3. George
4. Mary
5. Sam
6. Karen
7. Darren
8. Christopher
9. Emily
10. Marie
12. Jane
13. Claire
14. Harry
15. Lucy
16. Bruce
17. Ned
18. Elaine
19. Rudy
20. Alex

Why must you use a nonparametric test to determine whether there is a significant difference between the men and the women in terms of attentiveness? What test will you use?

4. You learn that these same 20 students are also taking a beginning math class. Is there a relationship between attentiveness level in the two classes? You ask the math professor to do the same kind of ranking as was done in the English class, and the data look like this:

1. Ann
2. Alex
4. Christopher
5. Marie
6. Darren
7. Bruce
8. George
9. Elaine
10. Sue
11. Jane
12. Karen
13. Lucy
14. Claire
15. Mary
16. Emily
17. Harry
18. Ned
19. Sam
20. Rudy

What is the correlation between the two sets of rankings? Is the relationship between behavior in the two classes significant?

5. The conductor of a small community orchestra thought he was noticing a pattern in arrival times for rehearsal: The women musicians seemed, on the average, to arrive earlier than the men. To check out this hypothesis, she asked the musicians to sign in as soon as they arrived at one of the rehearsals, and this is what the sign-in sheet looked like: Gloria, Enrico, Florence, Tomas, Sylvia, Sara, Kathryn, Henry, Amos, Charles, Curtis, Bradley, Phyllis, Elmer, and Ed. Does this list support his hypothesis?

6. A publisher is interested in the relationship between how much a textbook is used and how attractive its illustrations are. He has a group of 11th-grade students estimate how much they used their textbooks, and calculates overall rankings of text-book use. He also asks a panel of judges to rank the same textbooks in order of attractiveness of illustrations.
Here's what he found (low numbers indicate a favorable ranking):

Book Usage Ranking Illustration Ranking
Computing and You 1 7
History of Western Civilization 2 2
Trigonometry 3 8
World Literature 4 1
U.S. Government 5 6
Communication in Groups 6 3
Write On! 7 4
Personal Health 8 5

What can he conclude?

7. As a demonstration of randomness, a math teacher put 10 black and 10 white beans in a jar, shook them up, and then had a blindfolded student draw them out one at a time. The beans were drawn in the following order: W, B, B, B, B, W, W, W, B, W, B, B, W, W, B, B, W, W, B, W. He assigned each bean a number according to the order in which it was drawn, and then divided them into a group of black and a group of white beans. Then he did a Mann-Whitney U test to determine whether the beans were drawn in an order that was other than random. What result did the test yield?

9. At O-Y-Didicum Summer Camp, cabins were rated at the beginning of each week for general neatness. One of the counselors, who happened to be interested in statistics, decided to compare a set of these ratings with the camping experience of the campers. After reranking the cabins in terms of camping experience, the data looked like this:

Cabin Neatness Ranking Experience Ranking
Jays 1 6
Hawks 2 5
Buzzards 3 7
Eagles 4 3
Robins 5 4
Ducks 6 1
Swans 7 2

What can the counselor conclude about the relationship between neatness and participation?

10. The research committee of the Tight Tummy Club decided to find out if dessert choices are related to marital status. At their annual banquet, they kept track of who ordered what for dessert; they then used club registration information to find out people's marital status. Their final data were as follows:

Single Married Divorced Widowed Totals
Pie 3 5 4 2 14
Cake 1 4 2 3 10
Ice cream 4 2 2 1 9
Fresh fruit 12 1 10 4 27
Totals 20 12 18 10 60

Do these data support the hypothesis that dessert choice and marital status are related?