Graduate Statistics Homework Help

Complete the following exercises located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.

Show all relevant work; use the equation editor in Microsoft Word when necessary.

1. Chapter 19, numbers 19.9, 19.10, 19.13, 19.14, and 19.16

2. Chapter 20, numbers 20.5, 20.6, 20.7, and 20.10

19.9 Randomly selected records of 140 convicted criminals reveal that their crimes were committed on the following days of the week:

(a) Using the .01 level of significance, test the null hypothesis that in the underlying population, crimes are equally likely to be committed on any day of the week.

(b) Specify the approximate p-value for this test result.

(c) How might this result be reported in the literature?

*19.10 A number of investigators have reported a tendency for more people to die (from natural causes, such as cancer and strokes) after, rather than before, a major holiday. This post-holiday death peak has been attributed to a number of factors, including the willful postponement of death until after the holiday, as well as holiday stress and post-holiday depression. Writing in the Journal of the American Medical Association (April 11, 1990), Phillips and Smith report that among a total of 103 elderly California women of Chinese descent who died of natural causes within one week of the Harvest Moon Festival, only 33 died the week before, while 70 died the week after.

(a) Using the .05 level of significance, test the null hypothesis that, in the underlying population, people are equally likely to die either the week before or the week after this holiday.

(b) Specify the approximate p-value for this test result.

(c) How might this result be reported in the literature?

*19.13 Students are classified according to religious preference (Buddhist, Jewish, Protestant, Roman Catholic, or Other) and political affiliation (Democrat, Republican, Independent, or Other).

(a) Is anything suspicious about these observed frequencies?

(b) Using the .05 level of significance, test the null hypothesis that these two variables are independent.

(c) If appropriate, estimate the effect size.

*19.14 In 1912 over 800 passengers perished after the ocean liner Titanic collided with an iceberg and sank. The following table compares the survival frequencies of cabin and steerage passengers.

(a) Using the .05 level of significance, test the null hypothesis that survival rates are independent of the passengers’ accommodations (cabin or steerage).

(b) Assuming a significant χ2, estimate the strength of the relationship.

(c) To more fully appreciate the importance of this relationship, calculate an odds ratio to determine how much more likely a cabin passenger is to have survived than a steerage passenger.

19.16 Test the null hypothesis at the .01 level of significance that the distribution of blood types for college students complies with the proportions described in the blood bank bulletin, namely, .44 for O, .41 for A, .10 for B, and .05 for AB. Now, however, assume that the results are available for a random sample of only 60 students. The results are as follows: 27 for O, 26 for A, 4 for B, and 3 for AB. NOTE: The expected frequency for AB, (.05)(60) = 3, is less than 5, the smallest permissible expected frequency. Create a sufficiently large expected frequency by combining B and AB blood types.

20.5 A group of high-risk automobile drivers (with three moving violations in one year) are required, according to random assignment, either to attend a traffic school or to perform supervised volunteer work. During the subsequent five-year period, these same drivers were cited for the following number of moving violations:

(a) Why might the Mann–Whitney U test be preferred to the t test for these data?

(b) Use U to test the null hypothesis at the .05 level of significance

(c) Specify the approximate p-value for this test result.

20.6 A social psychologist wishes to test the assertion that our attitude toward other people tends to reflect our perception of their attitude toward us. A randomly selected member of each of 12 couples who live together is told (in private) that his or her partner has rated that person at the high end of a 0 to 100 scale of trustworthiness. The other member is told (also in private) that his or her partner has rated that person at the low end of the trustworthiness scale. Each person is then asked to estimate, in turn, the trustworthiness of his or her partner, yielding the following results. (According to the original assertion, the people in the trustworthy condition should give higher ratings than should their partners in the untrustworthy condition.)

(a) Use T to test the null hypothesis at the .01 level.

(b) Specify the approximate p-value for this test result.

20.7 Does background music influence the scores of college students on a reading comprehension test? Sets of 10 randomly selected students take a reading comprehension test with rock, country-western, or classical music in the back-ground. The results are as follows (higher scores reflect better comprehension)

(a) Why might the H test be preferred to the F test for these data?

(b) Use H to test the null hypothesis at the .05 level of significance

20.10 Use H rather than F to test the weight change data recorded in Review Question 16.13 on page 321.