Lab Assignment #3 for Chapter 9 MATH
1342 – Statistics
Instructor: David Katz
This lab assignment is to analyze a current events article that uses statistics to compare two proportions. Limit yourself to one short article that uses some type of hypothesis test. Usually students use the hypothesis testing methods of section 9-2. Your current event assignment should include these parts:
1) Copy of the Article – you may look for a short article in the newspaper, Internet, or similar source. You may even use a memo or policy document from your work. For starters, try these sources:
http://www.cancer.gov/clinicaltrials/results
Any prescription drug website, etc.
2) Citation Information – state the article’s title, publisher, author(s), date of publication, and URL if available.
3) Summary of the Statistics Problem - summarize in 3 or 4 sentences the hypothesis test included or implied in the article. Include in your summary which people fall into which group. For example, let group1 in your report represent the test group and let group 2 represent the placebo group, or vice versa.
4) Verification of the Statistical Method – show the mathematics behind the hypothesis test based on the given information in the article. Be sure to verify that the prerequisites of page 457 are satisfied before you proceed with your lab.
5) Conclusion – write one or two sentences that either support or refute the conclusion in the article.
How You Are Graded
(e.g., 48 out of 50 total points equals a grade of 96):
Item Points
- Summary of Article 5
- Citation, or Copy of Article 5
- State that sample data came from two independent and random group of individuals 5
- Verify and state that sample size is large enough 5
- Identify
and label the n, p-hat, q-hat, x
for group 1 and for group 2 5
- State the hypotheses and identify your claim 5
- Choose an appropriate a 5
- Show how you computed your test statistic, critical value, and/or or P-value 5
- Explain why you should reject or fail to reject the H0 5
- State your final conclusion in lay, non-technical terms 5
TOTAL POINTS 50
Typing the report is not necessary, but remember neatness counts! If I cannot read your report, I cannot grade it! Your finished report should be about 1-2 pages.
I encourage you to work together with your classmates to help write up the lab and/or find good articles with data tables. However, please don’t just copy verbatim a classmate’s lab report and hand it in as your own!
A sample homework assignment follows.
This excerpt from The
Dallas Morning News satisfies parts
(1) and (2) of the assignment.
Discoveries
briefs
Depressed elderly helped in home program study
A home-based program aimed at isolated elderly people can reduce symptoms of minor depression and improve health status, new research shows.
The study, led by Paul Ciechanowski of the
The program featured a behavioral treatment to help patients identify and address daily problems, and goal-setting to encourage participants to engage in pleasing activities. The program also helped patients develop a regimen of physical activity and to seek social interaction. Antidepressants were sometimes recommended, or doses were adjusted.
Compared with 66 patients who received usual care for their condition, the 72 patients in the program were far more likely to have at least a 50 percent reduction in depressive symptoms. More than one-third of the patients in the program completely overcame their depression, compared with 12 percent in the group getting the usual care.
The full study, appearing in the current issue of The Journal of the American Medical Association, can be read at http://jama. ama-assn.org/cgi/content/full/ 291/13/1569.
Karen Patterson
Summary of the Statistics
This article compares two sample proportions from a treatment plan for depression. In one sample, 12% of 66 patients experienced full recovery with the usual treatment program. In the second sample, 34% of 72 patients experienced full recovery with the new treatment program. The article claims that the new treatment program offers a statistically improved chance of recovery.
The Mathematics
Let 
the proportion for the
first sample.
Let 
the proportion for the
second sample.
Note that 
and 
. (Also check q-hat!)
Since these two sample proportions come from independent groups, and because the number of successes and failures in each sample is greater than five, we can conclude the sample sizes are large enough and that we can use the hypothesis testing methods of section 8-2 to compare these two proportions.
Let’s assume a significance level of a = 0.05.
The hypotheses are:
The pooled estimate of p1 and p2 is 
and so
.
Thus the test statistic z is:
The P-value associated with this test statistic » 0.0011, which is less than the level of significance. Thus, we reject the null hypothesis.
Conclusion
The sample data supports the article’s claim that the new method of treating depression offers a greater recovery rate than the usual method of treating depression.