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Chapter 12: Q. 12.1 (page 484)
What is meant by saying that a variable has a chi-square distribution?
If the distribution contains the shape of a special type of right skewed curve which is called the chi-square curve, then the variable is said to have a chi-square distribution. It is denoted by .
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In each of Exercises 12.24-12.33, apply the chi-square goodness-of-fit test, using either the critical-value approach or thevalue approach, to perform the required hypothesis test.
An American roulette wheel contains red numbers, black numbers, and green numbers. The following table shows the frequency with which the ball landed on each color in trials.
At the significance level, do the data suggest that the wheel is out of balance?
Road Rage. The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggressive driving and road rage. Road rage is defined as an incident in which an angry or impatient motorist or passenger intentionally injures or kills another motorist, passenger, or pedestrian, or attempts or threatens to injure or kill another motorist, passenger, or pedestrian." One aspect of the study was to investigate road rage as a function of the day of the week. The following table provides a frequency distribution for the days on which 69 road-rage incidents occurred.
Day | Frequency |
Sunday | 5 |
Monday | 5 |
Tuesday | 11 |
Wednesday | 12 |
Thursday | 11 |
Friday | 18 |
Saturday | 7 |
At the significance level, do the data provide sufficient evidence to conclude that road-rage incidents are more likely to occur on some days than on others?
A chi-square homogeneity test is to be conducted to decide whether a difference exists among the distributions of a variable of six populations. The variable has five possible values. What are the degrees of freedom for the x2-statistic?
In this exercise, you are to consider two variables, and defined on a hypothetical population. Following are the conditional distributions of the variable corresponding to each value of the variable.
a. Are the variables and associated? Explain your answer.
b. Determine the marginal distribution of.
c. Can you determine the marginal distribution of ? Explain your answer.
In given exercise use either the critical-value approach or the P-value approach to perform a chi square independence lest. provided the conditions for using the test are met.
Diabetes in Native Americans. Preventable chronic diseases are increasing rapidly in Native American populations, particularly diabetes. F. Gilliland et al. examined the diabetes issue in the paper "Preventative Health Care among Rural American Indians in New Mexico" (Preventative Medicine, Vol. 28, pp. 194-202). Following is a contingency table showing cross-classification of educational attainment and diabetic state for a sample of 1273 Native Americans (HS is high school).
At the 1% significance level, do the data provide sufficient evidence to conclude that an association exists between education level and diabetic state for native Americans?
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