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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
    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?

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    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.