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

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

11. Brad

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

3. Brad

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?

#### Solution Summary

Ten statistics problems involving Hypothesis Testing, Chi-Square, Nonparametric Tests and Mann-Whitney U Test are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.