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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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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)?
What鈥檚 your sign? The University of Chicago鈥檚 General Social Survey (GSS) is the nation鈥檚 most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random sample of people their astrological sign. Here are the counts of responses from a recent GSS of people:
If births are spread uniformly across the year, we expect all signs to be equally likely. Do these data provide convincing evidence at the significance level that all signs are not equally likely?
Regulating guns The National Gun Policy Survey asked a random sample of adults, "Do you think there should be a law that would ban possession of handguns except for the police and other authorized persons?" Here are the responses, broken down by the respondent's level of education:
Do these data provide convincing evidence at the level of an association between education level and opinion about a handgun ban in the adult population?
It鈥檚 hard for smokers to quit. Perhaps prescribing a drug to fight
depression will work as well as the usual nicotine patch. Perhaps combining the patch and
the drug will work better than either treatment alone. Here are data from a randomized,
double-blind trial that compared four treatments.
A 鈥渟uccess鈥� means that the subject did not smoke for a year following the start of the study.
a. Summarize these data in a two-way table.
b. Do the data provide convincing evidence of a difference in the effectiveness of the four
treatments at thesignificance level?
Tuition bills A random sample of U.S. adults was recently asked, 鈥淲ould you support or oppose major new spending by the federal government that would help undergraduates pay tuition at public colleges without needing loans?鈥� The two-way table shows the responses, grouped by age.
Do these data provide convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults?
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