Statistics Practice problems: P3, P4, P5, P6

P3. People spend huge sums of money (currently around $5 billion annually) for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study (based on data from Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). Use a 0.05 significance level to test the claim that those treated with magnets have a greater reduction in pain than those given a sham treatment (similar to a placebo). Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?

Reduction in pain level after magnet treatment: n = 20, x-bar = 0.49, s = 0.96
Reduction in pain level after sham treatment: n = 20, x-bar = 0.44, s = 1.4

P4. An experiment was conducted to test the effects of alcohol. The errors were recorded in a test of visual and motor skills for a treatment group of people who drank ethanol and another group give a placebo. The results are shown in the accompanying table (based on data from "Effects fo Alcohol Intoxication on Risk Taking, Strategy, and Error Rate in Visuomotor Performance," by Streufert et al., Journal of Applied Psychology, Vol. 77, No. 4). Construct a 95% confidence interval estimate of the difference between the two population means. Do the results support the common belief that drinking is hazardous for drivers, pilots, ship captains, and so on? Why or why not?

Treatment Group Placebo Group
n 1 = 22 n 2 = 22
x-bar 1 = 4.20 x-bar 2 = 1.71
s 1 = 2.20 s 2 = 0.72

P5. Refer to the data in the table that lists SAT scores before and after the sample of 10 students took a preparatory course (based on data from the College Board and "An Analysis of the Impact of Commercial Test Preparation Courses on SAT Scores," by Sesnowitz, Bernhardt, and Knain, American Educational Research Journal, Vol. 19, No. 3.)

Student A B C D E F G H I J
before 700 840 830 860 840 690 830 1180 930 1070
after 720 840 820 900 870 700 800 1200 950 1080

a. Is there sufficient evidence to conclude that the preparatory course is effective in raising scores? Use a 0.05 significance level.

b. Construct a 95% confidence interval estimate for the mean difference between the before and after scores. Write a statement that interprets the resulting confidence interval.

The following Minitab display resulted from an experiment in which 10 subjects were tested for motion sickness before and after taking the drug astemizole. The Minitab data column C3 consists of differences in the number of head movements that the subjects could endure without becoming nauseous. (The differences were obtained by subtracting the 'after' values from the 'before' values.)

a. Use a 0.05 significance level to test the claim that astemizole has an effect (for better or worse) on vulnerability to motion sickness. Based on the result, would you use astemizole if you were concerned about motion sickness while on a cruise ship?

b. Instead of testing from some effect (for better or worse), suppose we want to test the claim that astemizole is effective in preventing motion sickness? What is the p-value, and what do you conclude?

95% CI for mean difference: (-48.8, 33.8)
T-Test of mean difference = 0 (vs not = 0)
T-Value = -0.41
P-Value = 0.691

P6. The following Minitab display resulted from an experiment in which 10 subjects were tested for motion sickness before and after taking the drug astemizole. The Minitab data column C3 consists of differences in the number of head movements that the subjects could endure without becoming nauseous. (The differences were obtained by subtracting the 'after' values from the 'before' values.)

a. Use a 0.05 significance level to test the claim that astemizole has an effect (for better or worse) on vulnerability to motion sickness. Based on the result, would you use astemizole if you were concerned about motion sickness while on a cruise ship?

b. Instead of testing from some effect (for better or worse), suppose we want to test the claim that astemizole is effective in preventing motion sickness? What is the p-value, and what do you conclude?

95% CI for mean difference: (-48.8, 33.8)
T-Test of mean difference = 0 (vs not = 0)
T-Value = -0.41
P-Value = 0.691