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Chapter 11: Q. 52 (page 757)
How far away do you live? Conduct a follow-up analysis for the test in Exercise
We note that the expected value is higher than the observed counts of the public university for the category"over ",
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Inference recap (to ) In each of the following settings, state which inference procedure from Chapter you would use. Be specific. For example, you might answer, 鈥淭wo-sample z test for the difference between two proportions.鈥� You do not have to carry out any procedures.
a. What is the average voter turnout during an election? A random sample of cities was asked to report the percent of registered voters who voted in the most recent election.
b. Are blondes more likely to have a boyfriend than the rest of the single world? Independent random samples of blondes and nonblondes were asked whether they have a boyfriend.
Is your random number generator working? Use your calculator鈥檚 RandInt function to generate digits from to and store them in a list.
a. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator鈥檚 random number generator gives each digit an equal chance of being generated.
b. Carry out a test at the significance level. Hint: To obtain the observed
counts, make a histogram of the list containing the random digits, and use the trace feature to see how many of each digit were generated. You may have to adjust your window to go from with an increment of
c. Assuming that a student鈥檚 calculator is working properly, what is the probability that the student will make a Type I error in part (b)?
d. Suppose that students in an AP庐 Statistics class independently do this exercise for homework and that all of their calculators are working properly. Find the probability that at least one of them makes a Type I error.
Spinning heads? When a fair coin is flipped, we all know that the probability the coin lands on heads is However, what if a coin is spun? According to the article 鈥淓uro Coin Accused of Unfair Flipping鈥� in the New Scientist, two Polish math professors and their students spun a Belgian euro coin times. It landed heads times. One of the professors concluded that the coin was minted asymmetrically. A representative from the Belgian mint indicated the result was just chance. Assume that the conditions for inference are met.
a. Carry out a chi-square test for goodness of fit to test if heads and tails are equally likely when a euro coin is spun.
b. In Chapter Exercise you analyzed these data with a one-sample test for a proportion. The hypotheses were and
where the true proportion of heads. Calculate the statistic and P-value for this test. How do these values compare to the values from part (a)?
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?
Fruit flies Biologists wish to mate pairs of fruit flies having genetic makeup RrCc, indicating that each has one dominant gene (R) and one recessive gene (r) for eye color, along with one dominant (C) and one recessive (c) gene for wing type. Each offspring will receive one gene for each of the two traits from each parent, so the biologists predict that the following phenotypes should occur in a ratio of
Assume that the conditions for inference are met. Carry out a test at the significance level of the proposed genetic model.
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