Chapter 11: Q11-2-4BSC (page 533)
Is the hypothesis test described in Exercise 1 right tailed, left-tailed, or two-tailed? Explain your choice.
The hypothesis test is right-tailed.
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In his book Outliers,author Malcolm Gladwell argues that more
American-born baseball players have birth dates in the months immediately following July 31 because that was the age cutoff date for nonschool baseball leagues. The table below lists months of births for a sample of American-born baseball players and foreign-born baseball players. Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that months of births of baseball players are independent of whether they are born in America? Do the data appear to support Gladwell’s claim?
Born in America | Foreign Born | |
Jan. | 387 | 101 |
Feb. | 329 | 82 |
March | 366 | 85 |
April | 344 | 82 |
May | 336 | 94 |
June | 313 | 83 |
July | 313 | 59 |
Aug. | 503 | 91 |
Sept. | 421 | 70 |
Oct. | 434 | 100 |
Nov. | 398 | 103 |
Dec. | 371 | 82 |
Chocolate and Happiness In a survey sponsored by the Lindt chocolate company, 1708 women were surveyed and 85% of them said that chocolate made them happier.
a. Is there anything potentially wrong with this survey?
b. Of the 1708 women surveyed, what is the number of them who said that chocolate made them happier?
Chocolate and Happiness Use the results from part (b) of Cumulative Review Exercise 2 to test the claim that when asked, more than 80% of women say that chocolate makes them happier. Use a 0.01 significance level.
Benford’s Law. According to Benford’s law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. In Exercises 21–24, test for goodness-of-fit with the distribution described by Benford’s law.
Leading Digits | Benford's Law: Distributuon of leading digits |
1 | 30.10% |
2 | 17.60% |
3 | 12.50% |
4 | 9.70% |
5 | 7.90% |
6 | 6.70% |
7 | 5.80% |
8 | 5.10% |
9 | 4.60% |
Author’s Computer Files The author recorded the leading digits of the sizes of the electronic document files for the current edition of this book. The leading digits have frequencies of 55, 25, 17, 24, 18, 12, 12, 3, and 4 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively). Using a 0.05 significance level, test for goodness-of-fit with Benford’s law.
Equivalent Tests A\({\chi ^2}\)test involving a 2\( \times \)2 table is equivalent to the test for the differencebetween two proportions, as described in Section 9-1. Using the claim and table inExercise 9 “Four Quarters the Same as $1?” verify that the\({\chi ^2}\)test statistic and the zteststatistic (found from the test of equality of two proportions) are related as follows:\({z^2}\)=\({\chi ^2}\).
Also show that the critical values have that same relationship.
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