# Inferences from Two Samples

Module 4 Homework Assignment

1. Determine whether the samples are independent or dependent.

The effectiveness of a new headache medicine is tested by measuring the amount of time beforethe headache is cured for patients who use the medicine

and another group of patients who use aplacebo drug. Explain.

Solution:

2. Determine whether the samples are independent or dependent.

The effectiveness of a headache medicine is tested by measuring the intensity of a headache inpatients before and after drug treatment. The data

consist of before and after intensities for eachpatient.Explain.

Solution:

3. In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450people aged 25-29, 14% were smokers. Test the claim that

the proportion of smokers in the twoage groups is the same. Use a significance level of 0.01.Show all steps of the hypothesis test and all

calculations.

Solution:

4. A researcher wishes to determine whether people with high blood pressure can reduce theirblood pressure by following a particular diet. Use the

sample data below to perform all steps for hypothesis testing or construct a 99%confidence interval for µ1 – µ2 where µ1 and µ2 represent the mean

for the treatment group andthe control group respectively. Use the following t-distribution table –

http://www.itl.nist.gov/div898/handbook/eda/section3/eda3672.htm

Treatment Group Control Group
n1 = 85 n2 = 75
189.1 = 203.7
s1 = 38.7 s2 = 39.2

Solution:

For questions 5 – 9 below, use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that

two dependent samples have been randomly selected from normally distributed populations.

Five students took a math test before and after tutoring. Their scores were as follows.
Student A B C D E
Before 71 66 67 77 75
After 75 75 65 80 87

Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.

5. State the null and alternative hypotheses.
Solution:

6. Find d, , and sd,
Solution:

7. Find the value of the test statistic, t.
Solution: