ES9 Additional Exercises

Chapter 10

1. When the Dow Jones industrial average dropped 512 points on August 31, 1998, it was the largest point drop since the 554-point drop that hit the stock market on October 27, 1987. Prior to that drop, some experts had predicted a 9,500 Dow before the end of the year, but after the August slide, opinions changed. The consensus by many analysts seemed to be that the market would not bounce back in time to even approach the level predicted by earlier estimates. The bull was tired. Source: Fortune, “Requiem for the Bull”, September 28, 1998.

A random sample of 18 closing stock prices from the New York Stock Exchange was taken on August 25, 1998 (about one week prior to the “crash”), and again using the same stocks on September 15, 1998. Both dates are on a Tuesday. Results are shown in the table below:

a. On the basis of these data, construct a 90% confidence interval for the mean change from August 25 to September 15.

b. Can you conclude that the stock market was still suffering from the August 31 slide by September 15 or had it recovered? Explain.

2. An article titled, “Influencing Diet and Health Through Project LEAN” (Journal of Nutrition Education, July/August 1994) compared 28 individuals with borderline-high or high cholesterol levels before and after a nutrition education session. The participants’ cholesterol levels were significantly lowered, and the p-value was reported to be less than 0.001. A similar study involving 10 subjects was performed with the following cholesterol reading results:

Subject 1 2 3 4 5 6 7 8 9 10

Presession 295 279 250 235 255 290 310 260 275 240

Postsession 2665 266 245 240 230 230 235 250 250 215

Let d = presession cholesterol – postsession cholesterol.

Test the null hypothesis that the mean difference equals zero versus the alternative that the mean difference is positive at  = 0.05. Assume normality.

a. Solve using the p-value approach. b. Solve using the classical approach.

3. The two independent samples shown in the following table were obtained in order to estimate the difference between the two population means. Construct the 98% confidence interval.

Sample A 6 7 7 6 6 5 6 8 5 4

Sample B 7 2 4 3 3 5 4 6 4 2

4. An article titled "Stages of Change for Reducing Dietary Fat to 30% of Energy or Less" (Journal of the American Dietetic Association, Vol. 94, No. 10, October 1994) measured the energy from fat (expressed as a percent) for two different groups. Sample 1 was a random sample of 614 adults who responded to mailed questionnaires, and sample 2 was a convenience sample of 130 faculty, staff, and graduate students. The following table gives the percent of energy from fat for the two groups.

Group n Mean Standard Deviation

1 614 35.0 6.3

2 130 32.0 9.1

a. Construct the 95% confidence interval for ₁ - ₂.

b. Do these samples satisfy the assumptions for this confidence interval? Explain.

5. A study was designed to compare the attitudes of two groups of nursing students toward computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction through the use of statistical packages. Group 2 had taken a statistical methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Index (CAIN). The results were as follows:

Do the data show that the mean score for those with computer experience was significantly less than the mean score for those without computer experience? Use  = 0.05.

6. A 1998 study of the Y2K problem investigated consumer opinions over what should be done to handle the situation and who should be responsible for monitoring the progress. In response to the question, “Who should monitor the report on progress in solving the Y2K problem?”, 34% of the respondents surveyed felt that it was the government’s responsibility.

Source: Newsweek, “It’s Not My Problem”, October 5, 1998.

Suppose you believe that differences in opinion exist between rural and city dwellers on whether the government should monitor the Y2K problem. A study of 250 heads of households in the city and 200 rural heads of households are asked the above question. You find that 100 of the city dwellers and 64 of the rural dwellers believed that it was the government’s responsibility. Is there a significant difference in the opinions of the two groups? Use  = 0.05.

7. One of the most commonly seen applications of statistics is the poll percentages, reported in the news, of people who say, think or do some specific thing. So who does “know the American flag?” Two hundred adults in Erie County, NY were asked how many stars there are on the USA flag. The table below shows the number of adults belonging to each category. The sample results were tallied twice, by gender and by residence of adult answering question.

	Men	Women	City	Urban	Rural
n(Knew)	72	72	57	58	31
n(Didn’t know)	22	34	25	14	15

a. Is there a significant difference between the percentage of men and the percentage of women who answered the question correctly? Use  = 0.05.

b. Is there a difference between the percentage of city and the percentage of urban adults who answered the question correctly? Use  = 0.05.

8. Twelve automobiles were selected at random to test two new mixtures of unleaded gasoline. Each car was given a measured allotment of the first mixture, x, and driven; then the distance traveled was recorded. The second mixture, y, was immediately tested in the same manner. The order in which the x and y mixtures were tested was also randomly assigned. The results are given in the following table.

Car

Mixture 1 2 3 4 5 6 7 8 9 10 11 12

x 7.9 5.6 9.2 6.7 8.1 7.3 8.1 5.4 6.9 6.1 7.1 8.1

y 7.7 6.1 8.9 7.1 7.9 6.7 8.2 5.0 6.2 5.7 6.2 7.5

Can you conclude that there is no real difference in mileage obtained by these two gasoline mixtures at the 0.10 level of significance? Assume mileage is normal.

a. Solve using the p-value approach. b. Solve using the classical approach.

9. The following data were collected concerning waist sizes of men and women. Do these data present sufficient evidence to conclude that men have larger mean waist sizes than women at the 0.05 level of significance? Assume waist sizes are normally distributed.

34 32 35 32 32 34 36 30 38

Women 22 29 27 24 28 28

27 26 27 26 25