Inferences from Two Proportions and Samples
1
Task 1: Solve the following problems:
?  A student of the author surveyed her friends and found that among 20 males, 4 smoke and among
30 female friends, 6 smoke. Give two reasons why these results should not be used for a hypothesis
test of the claim that the proportions of male smokers and female smokers are equal.
?  Given a simple random sample of men and a simple random sample of women, we want to use a
0.05 significance level to test the claim that the percentage of men who smoke is equal to the
percentage of women who smoke. One approach is to use the P-value method of hypothesis
testing; a second approach is to use the traditional method of hypothesis testing; and a third
approach is to base the conclusion on the 95% confidence interval estimate of p1—p2. Will all three
approaches always result in the same conclusion? Explain.
Task 2: Solve the following problems:
?  The mean tar content of a simple random sample of 25 unfiltered king-size cigarettes is 21.1 mg,
with a standard deviation of 3.2 mg. The mean tar content of a simple random sample of 25 filtered
100 mm cigarettes is 13.2 mg with a standard deviation of 3.7 mg.
Assume that the two samples are independent, simple, random samples, selected from normally
distributed populations. Do not assume that the population standard deviations are equal.
o  Use a 0.05 significance level to test the claim that unfiltered king-size cigarettes have mean
tar content greater than that of filtered 100 mm cigarettes.
o  What does the result suggest about the effectiveness of cigarette filters?
?  Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms
of the same woman. Use a 0.05 significance level to test for a difference between the
measurements from the two arms. What do you conclude? Assume that the paired sample data are
simple random samples and that the differences have a distribution that is approximately normal.
Right Arm  102  101  94  79  79
Left Arm  175  169  182  146  144
MA3110: Module 4 Hypothesis Testing
Exercise 4.1
Inferences from Two Proportions and Samples
2
Submission Requirements:
?  Submit the assignment in a Microsoft Word or Excel document.
?  Show detailed steps and provide appropriate rationale with your answers.
Evaluation Criteria:
?  Correctly answered each question
?  Included appropriate steps or rationale to determine the answer to each question