Download Worksheet9a

Worksheet 9a – ph6450
Thinking about Null and Alternative Hypotheses
[Examples adapted from: Rosner, Fundamentals of Biostatistics (Chapter 7)
Pagano and Gauvereau, Principles of Biostatistics (Chapter 10)]
1. [R, Ex. 7.1] A current area of research interest is the familial aggregation of
cardiovascular disease risk, including serum lipid levels. Suppose mean cholesterol level
in U.S. children 0-18 years old is 175 mg/dL. 200 men who have died within the past 12
months from heart disease are sampled from death certificates filed with the state of MN.
Of those men, 67 are identified to have at least one living child 18 years old or younger.
One child is randomly selected for each man, and serum cholesterol is obtained from that
child. Sample mean cholesterol ( X ) and sample standard deviation in cholesterol (s) is
computed. Is the mean cholesterol of children like this (children of men who have died
from heart disease) greater than the mean cholesterol of children in general?
What is H0?
What is Ha?
What does μ represent?
What does μ0 represent?
Do we use a z-test or a t-test?
2. [R, Ex. 7.13] A new drug is being developed which may reduce infarct size for patients
who have had a myocardioal infarction within the past 24 hours. Suppose we know that
among patients treated with standard care, the mean infarct size is 25 ck-g-EQ/m2. and
standard deviation in infarct size is 16. In a sample of 38 patients treated with the new
drug, mean infarct size was 16. Do patients treated with the new drug have lower mean
infarct size than patients treated with standard care? (Assume patients treated with the
new drug have the same population standard deviation as patients treated with standard
care.)
What is H0?
What is Ha?
What does μ represent?
What does μ0 represent?
Do we use a z-test or a t-test?
3. According to the Centers for Disease Control (CDC), mean body mass index (BMI)
among US female Mexican-Americans age 20-39 years in 1999-2002 was 31.2 kg/m2. In
the same time frame, 57 females newly immigrated from Mexico in the same age group
were measured for BMI with a sample average of 28.2 kg/m2 and standard deviation 2.7
kg/m2. For this age group, do new female immigrants from Mexico have a different mean
BMI compared to female Mexican-Americans?
What is H0?
What is Ha?
What does μ represent?
What does μ0 represent?
Do we use a z-test or a t-test?
4. [P&G, Exercise 10.10] E. canis infection is a tick-borne disease of dogs that is sometimes
contracted by humans. Among non-infected humans, the distribution of white blood cell
counts has mean 7250 cells/mm3. In a sample of size 15 of infected persons, average
WBC count is 4767 cells/mm3 with standard deviation 3204 cells/mm3. Do persons with
this infection have a lower mean WBC count?
What is H0?
What is Ha?
What does μ represent?
What does μ0 represent?
Do we use a z-test or a t-test?