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Chapter 11: Q. 51 (page 757)
Where do you live? Conduct a follow-up analysis for the test in Exercise 49.
We note that the expected value is higher than the observed counts of females for the category "Parents' home".
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Stress and heart attacks You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:
One group took a four-month stress management program, another underwent a four-month exercise program, and the third received usual heart care from their personal physicians. In the next three years, only of the people in the stress management group suffered "cardiac events," defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, of the people in the exercise group and out of the patients in usual care suffered such events.
a. Use the information in the news article to make a two-way table that describes the study results.
b. Compare the success rates of the three treatments in preventing cardiac events.
c. Do the data provide convincing evidence at the level that the true success rates for patients like these are not the same for the three treatments?
Seagulls by the seashore Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of sand, mud, and rocks. The biologists chose seagulls at random. Each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. In all, seagulls landed on the sand, landed in the mud, and landed on the rocks.
a. Do these data provide convincing evidence that seagulls show a preference for where they land?
b. Relative to the proportion of each ground type on the shore, which type of ground do the seagulls seem to prefer the most? The least?
Fewer TVs? The United States Energy Information Administration periodically surveys a random sample of U.S. households to determine how they use energy. One of the variables they track is how many TVs are in a household (None, or more). The computer output compares the distribution of number of TVs for households in .
Cell Contents: Count
Expected count
Contribution to Chi-square
Chi-Squarerole="math" localid="1654195309908" , DF , P-Value
a. Which chi-square test is appropriate to analyze these data? Explain your answer.
b. Show how the numbers and were obtained for the cell.
c. Which cells contribute most to the chi-square test statistic? How do the observed and expected counts compare for these cells?
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver. The results are summarized in the following table.
The proportion of this city's population in each of the racial/ethnic categories listed is as follows.
We wish to test : The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city's population.
Assuming is true, what is the expected number of Hispanic drivers who would receive a ticket?
a.
b.
c.
d.
e.
Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of freshmen, sophomores, juniors, and seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. Here are the results:
The conditions for carrying out the chi-square test in Exercise T are:
I. Independent random samples from the populations of interest.
II. All sample sizes are less than of the populations of interest.
III. All expected counts are at least .
Which of the conditions is (are) satisfied in this case?
a. I only
b. II only
c. I and III only
d. II and III only
e. I, II, and III
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