Exercises 1 - eBay selling prices: For eBay auctions of the iPad2 64GB 3G Wi-Fi units, a sample was taken in July 2011 where the Buy-it-Now prices were (in dollars):
1388, 1199, 1100, 1099, 1088, 1049, 1026, 999, 998, 978, 949, 930
a. Explain what a parameter might represent that you could estimate with these data.
b. Find the point estimate of μ.
c. Find the standard deviation of the data and the standard error of the sample mean. Interpret.
d. Find the 95% confidence interval for μ. Interpret the interval in context.
Exercises 2 - Changing views of United States: The June 2003 report on Views of a Changing World, conducted by the Pew Global Attitudes Project (www.people-press.org), discussed changes in views of the United States by other countries. In the largest Muslim nation, Indonesia, a poll conducted in May 2003 after the Iraq war began reported that 83% had an unfavorable view of America, compared to 36% a year earlier. The 2003 result was claimed to have a margin of error of 3 percentage points. How can you approximate the sample size the study was based on?
Exercises 3 - In lab/discussion 2, you work with a small data file which contained data on N=20 participants from the Diabetes Self-Care Intervention Study, all of whom received the intervention. Two of the variables included measurements of hemoglobin A1c levels at two time points-before participating in the intervention and after. Thus, the timing of the A1c measurements around the intervention in this small sample of study participants constitutes a before/after (pretest/posttest) quasi-experimental design.
You also created a variable during this lab session measuring how much A1c changed from before the intervention to after for each person, which mathematically was the after- intervention A1c measurement minus the before-intervention measurement. You will use this variable as the RV in a one-sample t-test in which you test whether A1c changes significantly from before to after the intervention. Answer the following:
a. State the null and alternative hypotheses in words and statistical symbols (as you've seen on many lecture slides and lab instructions at this point).
b. Why is zero the appropriate null hypothesis value in this situation?
c. Run the one-sample t-test in STATA and display your output below:
d. Did A1c levels change significantly from before the intervention to after? Support your answer by reporting the sample mean change-in-A1c, its t-statistic and its applicable p-value. Is your decision to reject or retain the null hypothesis on the basis of these results?
e. State your conclusion conceptually. What do you conclude about the nature of the association (or lack of association) between receiving the intervention and changes in overall levels of A1c?
Exercises 4- Surgery versus placebo for knee pain: Refer to Example on whether arthroscopic surgery is better than placebo. The following table shows the pain scores one year after surgery. Using software (such as MINITAB) that can conduct analyses using summary statistics, compare the placebo to the debridement group using a 95% confidence interval. Use the method that assumes equal population standard deviations. Explain how to interpret the interval found using software.
| Knee Pain Score |
| Group |
Sample Size |
Mean |
Standard Deviation |
| Placebo |
6 |
48.9 |
21.9 |
| Arthroscopic-lavagwe |
61 |
54.8 |
19.8 |
| Arthroscopic-debridement |
59 |
51.7 |
22.4 |
More knee pain: Compare the placebo to the debridement group using a significance test. State the assumptions, and explain how to interpret the P-value.
Exercises 5- Aspirin and heart attacks for women: A study in the New England Journal of Medicine compared cardiovascular events for treatments of low-dose aspirin or placebo among 39, 876 healthy female health care providers foray average duration of about 10 years. Results indicated that women receiving aspirin and those receiving placebo did not differ for rates of a first major cardiovascular event, death from cardiovascular causes, or fatal or non-fatal heart attacks. However, women receiving aspirin had lower rates of stroke than those receiving placebo (Data from N. Engl. J. Med., vol. 352, 2005, pp. 1293-1304).
| Women's Aspirin Data |
|
Cardiovascular Events |
| Group |
Mini-Stroke |
Stroke |
No Strokes |
| Placebo |
240 |
259 |
19443 |
| Aspirin |
185 |
219 |
19530 |
a. Use software to test independence. Show (i) assumptions (ii) hypotheses (iii) test statistic, (iv) P-value (v) conclusion in the context of this study.
b. Describe the association by finding and interpreting the relative risk for the stroke category.