Question

1. For each of the following scenarios, identify:

• the population of interest,
• the outcome variable being measured on each observational unit,
• whether the outcome variable being measured is categorical or quantitative/Continuous,
• the parameter of interest, define both in words and using the appropriate statistical symbol (π, π1 -π2, µ, µ1 - µ2, or µd), and
• the null and alternative hypotheses, written in correct statistical notation (not in words)

Name the hypothesis test you would use. For example, some tests we have learned are:

• one-sample t-test of the population mean
• one sample z-test of the population proportion
• independent two-sample pooled t-test for the difference between population means
• independent two-sample unpooled z-test for the difference between population means
• Paired t-test for 2 dependent samples
• independent two-sample z-test for the difference between population proportions
• McNemar test for dependent proportions
• Chi-square test for homogeneity
• Chi-square test for of independence

1. A study was conducted looking at risk factors for HIV infection among intravenous drug users enrolled in a methadone program. Data was collected on family income (<$10,000, $10,000-$20,000, >$20,000) and the HIV antibody status (positive/negative) as assessed by blood testing at one point in time.

2. Suppose from large studies we know that the mean cholesterol in children aged 2-14 is 175 mg/dL. We wish to see if there is a familial aggregation of cholesterol level. We identify a group of fathers who have elevated cholesterol levels (>250 mg/dL) and have had a heart attack and measure the cholesterol levels of their offspring within the 2-14 age range.

3. To examine the safety of working in a nuclear power plant, we assess deaths due to cancer among all deaths at a particular power plant. Based on vital statistics, about 20% of all deaths can be attributed to some form of cancer.

4. We wish to assess whether there is a relationship between bone mineral density and cigarette smoking. To approach this problem we have a sample of twin pairs, where one twin is a heavy smoking twin and the other twin is a lighter smoking.

5. A randomized trial study is performed to compare survival (time to death in months) two chemotherapy drugs (A vs B) among cancer patients. A sample of cancer patients are randomly assigned to treatment A or B.

Answer 1

a.) The hypothesis is Chisquare test for homogeneity.The outcome variable is standard deviation of sample population s^{​​​​​​2}.Outcome variable is quantitative.

d.)The hypothesis is Chisquare test for homogeneity.The outcome variable is standard deviation of sample population s^{​​​​​​2}. Outcome variable is quantitative.

e.) The hypothesis is Chisquare test for independence. Outcome variable is s^{​​​​​​2}. Outcome variable is quanitative.

b.)The hypothesis is one sample t distribution.outcome variable is . Outcome variable is quantitative.