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# Test of hypothesis, Sample Size

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1. Erthromyacine is a drug that has been related with side effects during pregnancy. Assume that 30% of women experience side effects between the 24th and 28th week of pregnancy. Furthermore suppose that of 200 women who are taking the drug 110 complain of nausea. Test the hypothesis that the incidence rate of nausea for the drug group is the same as a typical pregnant woman.

2.High cholesterol have for some time been suspected to cause heart attacks. The problem is that it is difficult to factor out other aspects. suppose we isolate 100 men who have high cholesterol levels and can predict on the basis of other factors that 10% of these men will have a heart attack in the next five years.

Suppose that the incidence rate of heart attacks in the next five years is 13%. Is the finding indicative of anything about cholesterol?
Suppose we had 1000 men istead of 100 men and also found an incidence rate of 13%. Is this finding indicative of anything about cholesterol?
How large a sample would be needed to have an 80% chance of finding a signifigant difference if the true rate of heart disease in this group id 13%

3.Previous studies have show that supplements of diet may lower serum-cholesterol levels. It is not known wether or not someones cholesterol level is decreased by the replacement of bran with another food or if the bran actually reduces it. a study was done on 20 healthy subjects between ages 23-49 years old . below are the results
total cholesterol n baseline high fiber low fiber (diff high-low fiber) (diff high-baseline) (diff low -baseline)
20 186+-31 172+-28 172+-25 -1(-8,+7 ) -14(-21,-7) -13(-20,-6)
Test the hypothesis that the high fiber diet has an effect on cholesterol levels as compared with baseline (report your results as p<0.05 or p>.05)

4. A study was done in Pittsburg that looked at various cardiovascular risk factors in children and in their first five years of life. Their heart rates were measured at 5,15,24 months.
race mean (beats per minute) sd n
white 125 11 218
black 133 12 156
Test for a signifigance in mean heart rate between white and black newborns report a p-value for the test performed in problem 8.29

5. Group one consists of 23 nonsmoking children 5-9 years of age both of whose parents smoke who have a mean fev of 2.1 and a sd of 0.7. Group 2 consists of 20 nonsmoking children comparable in age, neither of whose parents smoke. They have a mean fev of 2.3L and sd of 0.4L.
a. what is the appropriate nul and alternative hypothesis in prob 8.59?
b. What is the appropriate test procedure for the hypothesis in prob 8.59?
c. Carry out the prob in b using the critical value method
d. provide a 95% confidence interval for the true mean difference between 5-9 year old children whose parents smoke and comparable children whose parents smoke and comparable to children whose parents do not smoke
e. If this is regarded as a pilot study then how many children are needed in each group to have a 95% chance of detecting a signifigant difference using a two sided test with alpha=.05
f. Answer the question in problem e if the investigators intend to use a one sided rather than a two sided test.
Suppose 40 children both of whose parents smoke and 50 whose parents do not are recruited for the study
g. How much pwer would such a study have using a two-sided test with sig level= .05, assuming that the estimates of the pop parameters in the pilot study are correct.
h. Answer g using a one sided test