Statistics - Trevian

MA3110: Module 4 Hypothesis Testing

Exercise 4.1

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 1 0 2 1 0 1 9 4 7 9 7 9

Left Arm 1 7 5 1 6 9 1 8 2 1 4 6 1 4 4

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