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Cleopatra74
1. The data in the table are a sample from a larger data set collected on people discharged from a selected Pennsylvania hospital as part of a retrospective chart review of antibiotic usage in hospitals.
Hospital-stay data
ID number |
Duration of hospital stay |
Received Antibiotics? |
1 |
5 |
no |
2 |
10 |
no |
3 |
6 |
no |
4 |
11 |
no |
5 |
5 |
no |
6 |
14 |
yes |
7 |
30 |
yes |
8 |
11 |
no |
9 |
17 |
no |
10 |
3 |
no |
11 |
9 |
no |
12 |
3 |
no |
13 |
8 |
yes |
14 |
8 |
yes |
15 |
5 |
no |
16 |
5 |
no |
17 |
7 |
yes |
18 |
4 |
no |
19 |
3 |
yes |
20 |
7 |
no |
21 |
9 |
no |
22 |
11 |
yes |
23 |
11 |
no |
24 |
9 |
no |
25 |
4 |
no |
Compute the mean and median for the duration of hospitalization for the 25 patients.
2. Using the table from Problem 1, compute the standard deviation and range for the duration of hospitalization for the 25 patients.
3. Select all types of measures of location:
Mode
Median
Standard Deviation
Arithmetic Mean
Variance
4. Suppose 6 of 15 students in a grade-school class develop influenza, whereas 20% of grade-school students nationwide a develop influenza. Is there evidence of an excessive number of cases in the class? That is, what is the probability of obtaining at least 6 cases in this class if the nationwide rate holds true?
5. Using the data from Problem 4, what is the expected number of students in the class who will develop influenza?
6.Two events A and B are ___________________________ if they cannot both happen at the same time. (Hint: the answer is two words).
6. Serum cholesterol is an important risk factor for coronary disease. We can show that serum cholesterol is approximately normally distributed, with mean= 219 mg/dL and standard deviation =50 mg/dL.
7. What proportion of the general population has borderline high-cholesterol levels--that is, > 200 but < 250 mg/dL?
0.380
0.648
0.7324
0.620
8. Much discussion has taken place concerning possible health hazards from exposure to anesthetic gases. In one study conducted in 1972, 525 Michigan nurse anesthetists were surveyed by mail questionnaires and telephone interviews to determine the incidence rate of cancer. Of this group, 7 women reported having a new malignancy other than skin cancer during 1971.
What is the best estimate of the 1971 incidence rate from these data?
9. Using the data from Problem 8, provide a 95% confidence interval for the true incidence rate.
10. Choose the correct word for the following sentence: If the results of a previous trial does not affect the result of the following trial, then the results are __________________ (dependent/independent).
Independent or Dependent
11. Approximately ___% of the probability mass falls within two standard deviations (2 ) of the mean of a random variable.
95%
50%
68%
99.7
12. Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9 to 11 year old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population.
State the hypotheses that we can use to consider this question. Perform the hypothesis test using the critical-value method with an alpha of 0.05, and summarize your findings. Report the p-value for this test (may give a range that includes the p-value)
13. A clinical trial is called _____________________ if neither the physician nor the patient knows what treatment he or she is getting. (Hint: the blank is two words)
14. In a study, 28 adults with mild periodontal disease are assessed before and 6 months after implementation of a dental-education program intended to promote better oral hygiene. After 6 months, periodontal status improved in 15 patients, declined in 8, and remained the same in 5.
Assess the impact of the program statistically (use a two-sided test)
15. Two drugs (A, B) are compared for the medical treatment of duodenal ulcer. For this purpose, patients are carefully matched with regard to age, gender, and clinical condition. The treatment results based on 200 matched pairs show that for 89 matched pairs both treatments are effective; for 90 matched pairs both treatments are ineffective; for 5 matched pairs drug A is effective, whereas drug B is ineffective; and for 16 matched pairs drug B is effective, whereas drug A is ineffective.
What test procedure can be used to assess the results?
McNemar’s test for correlated proportions
Fisher’s exact Test
The Paired t Test
The Sign Test
16. The standard screening test for Down's syndrome is based on a combination of maternal age and the level of serum alpha-fetoprotein. Using this test 80% of Down's syndrome cases can be identified, while 5% of normals are detected as positive.
What is the sensitivity and specificity of the test?
17. Lutein, an important carotenoid in the maintenance of ocular health, has been found postmortem in th macula of eyes. Hence, a study is planned to supplement patients with high doses of lutein in capsule form to possibly prevent age-related macular degeneration, an important eye disease that can cause partial or total blindness in large numbers of elderly people.
To assess compliance in study participants, a blood sample will be drawn. It is estimated that a serum lutein would indicate that a participant is taking study medication.
The study began in 1999. A test sample of 9 participants had their lutein level measured in 1999 and again in 2003. The researchers found a calibration error in the 1999 assays, but the 2003 assays were correct. The data are shown in the table below.
Serum-lutein data analyzed in 1999 and 2003
Sample |
1999 Serum-lutein level |
2003 Serum-lutein level |
1 |
3.5 |
6.4 |
2 |
2.9 |
7.5 |
3 |
4.1 |
8.4 |
4 |
5.1 |
9.6 |
5 |
6.4 |
12.0 |
6 |
1.9 |
4.2 |
7 |
1.3 |
3.1 |
8 |
4.1 |
6.3 |
9 |
2.3 |
4.4 |
Mean |
3.511 |
6.878 |
sd |
1.616 |
2.839 |
Using regression methods, derive a calibration formula predicting the 2003 level as a function of the 199 level.
y=0.999+1.674x
y=-0.999+1.674x
y=0.999-1.674x
y=0.999x+1.674
18. The probability of a _________________ (Type 1 error/Type 2 error) is the probability of accepting the null hypothesis when H_1 is true.
19. In a ________________ study the same group of people is followed over time.
Longitudinal
Cross-sectional
Paired
Double blind
20. A recent article by Kenfield et al. studied the relationship between various aspects of smoking and mortality among 104,519 women in the Nurses' Health Study (NHS) from 1980-2004. One issue is whether there is a mortality benefit from quitting smoking vs. continuing to smoke and, if so, how long it takes for the mortality experience of former smokers to approximate that to never smokers. The data in the table below were presented comparing former smokers with current smokers.
Relationship of time since quitting to total mortality
Number of deaths |
Number of person-years of follow-up |
|
Current smokers |
3,602 |
420,761 |
Former smokers |
|
|
Quit <5 yrs |
889 |
124,095 |
Quit 5-9 yrs |
669 |
113,056 |
Quit 10-14 yrs |
590 |
111,701 |
Quit 15-19 yrs |
541 |
117,914 |
Quit 20+ yrs |
1,707 |
336,177 |
What is the estimated mortality rate and 95% confidence interval per 1000 person-years among current smokers?