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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 |
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 |
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 |
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 |
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.
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