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Testing of hypothesis problems from bio statistics

See attached file for full problem description.

In a study designed to compare the efficacy of two drugs in lowering blood pressure, patients were paired according to their gender, age and disease severity. Patients within each pair were randomly allocated to one of the two drugs. Summary statistics for the decrease in blood pressure over 6 months are recorded below.

DECREASE IN BLOOD PRESSURE (mmHg)

PAIR DRUGA DRUGB

1 25 10

2 55 44

3 35 11

4 25 19

n 4 4

Mean 35 21

Standard 14.14 15.85
Deviation

Test the hypothesis that the mean decrease in blood pressure is the same in the two groups.

A study is designed to compare the ability of a drug and dietary intervention to decrease weight. Patients are randomly allocated to two groups, 16 to a drug therapy and 25 to a special diet. Summary statistics for the weight variable are given below.

DRUG DIET
6-Month 6-Month
Pre Post Change Pre Post Change

n 16 16 16 25 25 25

Mean 140 132 8 138 126 12

Standard 4.2 5.3 1.25 5.3 4.9 1.20
Error

Test the hypothesis that the mean weight change is the same in each group.

A study was designed to compare the ability of two drugs to provide a clinically important reduction in headache pain over a 2-week period. Each patient received both drugs, one of the drugs for a 2-week period, followed by a 1-week rest and then the other drug for a 2-week period. The order of drugs was random.

Improve on Drug B

Yes No

Yes 7 13 20
Improve on
Drug A
No 3 27 30

10 40 50

Use an approximate method and an exact method to test the hypothesis that the probability of an important clinical outcome is the same in each group.

In a group of 50 workers exposed to a toxin 30% had shortness of breath (SOB) compared to only 10% of 40 unexposed workers. Estimate the relative risk of SOB associated with toxin exposure. Use the confidence interval of the relative risk to test the hypothesis that the relative risk is equal to 1.

The slope between the change in FVC (DFC) over a 2-hour exposure and the concentration of ozone is 0.20. Summary statistics are:

SUBJECT OZONE DFVC RESIDUAL
CONC

1 0.0 * 0.0
2 2.0 * 0.2
3 4.0 * -0.1
4 6.0 * -0.2
5 8.0 * 0.1

Test the hypothesis of no association between ozone and change in FVC using

(a) Test of Significance (b) Confidence interval

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Solution Summary

The solution gives the details of testing of hypothesis problems from bio statistics. Confidence Interval, test statistic, student t test, null hypothesis, critical value etc are given with interpretations.

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