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A manager of a sports club keeps information concerning the main sport in which members participate and their ages. To test whether there is a relationship between the age of a member and his or her choice of sport, 643 members of the sports club are randomly selected. Conduct a test for independence.

Sport 18 - 25 26 - 30 31 - 40 41 and over
racquetball 42 58 30 46
tennis 58 76 38 65
swimming 72 60 65 33
  • 6
  • 25.21
  • 0.0003
  • Decision: Reject null

A major food manufacturer is concerned that the sales for its skinny French fries have been decreasing. As a part of a feasibility study, the company conducts research into the types of fries sold across the country to determine if the type of fries sold is independent of the area of the country. The results of the study are below. Conduct a test for independence.

Type of Fries Northeast South Central West
skinny fries 70 50 20 25
curly fries 100 60 15 30
steak fries 20 40 10 10

According to Dan Lenard, an independent insurance agent in the Buffalo, N.Y. area, the following is a breakdown of the amount of life insurance purchased by males in the following age groups. He is interested in whether the age of the male and the amount of life insurance purchased are independent events. Conduct a test for independence.

Age of Males None <$200,000 $200,000 - $400,000 $401,001 - $1,000,000 $1,000,000 +
20 - 29 40 15 40 0 5
30 - 39 35 5 20 20 10
40 - 49 20 0 30 0 30
50 + 40 30 15 15 10
  • 12
  • 125.74
  • 0
  • Decision: Reject null

Suppose that 600 thirty–year–olds were surveyed to determine whether or not there is a relationship between the level of education an individual has and salary. Conduct a test for independence.

Annual Salary Not a high school graduate High school graduate College graduate Masters or doctorate
<$30,000 15 25 10 5
$30,000 - $40,000 20 40 70 30
$40,000 - $50,000 10 20 40 55
$50,000 - $60,000 5 10 20 60
$60,000 + 0 5 10 150

A Psychologist is interested in testing whether there is a difference in the distribution of personality types for business majors and social science majors. The results of the study are shown below. Conduct a Test of Homogeneity. Test at a 5% level of significance.

Open Conscientious Extrovert Agreeable Neurotic
Business 41 52 46 61 58
Social Science 72 75 63 80 65

  • 4
  • Chi-Square with df = 4
  • 3.01
  • p-value = 0.5568

  • ii. Do not reject the null hypothesis.
    iv. There is insufficient evidence to conclude that the distribution of personality types is different for business and social science majors.

Do men and women select different breakfasts? The breakfast ordered by randomly selected men and women at a popular breakfast place is shown below. Conduct a test of homogeneity. Test at a 5% level of significance

French Toast Pancakes Waffles Omelettes
Men 47 35 28 53
Women 65 59 55 60

  • 3
  • 4.01
  • p-value = 0.2601

  • ii. Do not reject the null hypothesis.
    iv. There is insufficient evidence to conclude that the distribution of breakfast ordered is different for men and women.

Is there a difference between the distribution of community college statistics students and the distribution of university statistics students in what technology they use on their homework? Of the randomly selected community college students 43 used a computer, 102 used a calculator with built in statistics functions, and 65 used a table from the textbook. Of the randomly selected university students 28 used a computer, 33 used a calculator with built in statistics functions, and 40 used a table from the textbook. Conduct an appropriate hypothesis test using a 0.05 level of significance.

  • 2
  • 7.05
  • p-value = 0.0294

  • ii. Reject the null hypothesis.
    iv. There is sufficient evidence to conclude that the distribution of technology use for statistics homework is not the same for statistics students at community colleges and at universities.

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Source:  OpenStax, Collaborative statistics (with edits: teegarden). OpenStax CNX. Jul 20, 2009 Download for free at http://legacy.cnx.org/content/col10561/1.3
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