Week 4 Assignment 4.1
EG381: Module 4 Hypothesis Testing
Exercise 4.1 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.
First, the sample is not random, it is a convenience sample and therefore cannot be trusted. Second, np҄ = x = 4 < 5, therefore the normal distribution cannot be used to approximate the binomial distribution.
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.
As long as the test is two tailed (so that a confidence interval can be used) and since α = .05 and percent confidence = 1 - .05 = .95, then yes, the results will NEARLY ALWAYS be the same between traditional approach and confidence interval approach. Also it will NEARLY ALWAYS be the same between the p-value approach and the confidence interval approach. The reason that I say "almost always" is that the standard error formula for p҄1-p҄2 is slightly different for the confidence interval approach than for the hypothesis testing approach.
The result will ALWAYS be the same between the traditional and p-value approaches whether the test is two tailed or not.
Criteria for rejecting Ho:
Traditional approach: α = .05, reject Ho if z < -1.96 or z > 1.96
P-value approach: Reject Ho if p-value < .05 (which only occurs if z < -1.96 or z > 1.96).
Confidence
Exercise 4.1 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.
First, the sample is not random, it is a convenience sample and therefore cannot be trusted. Second, np҄ = x = 4 < 5, therefore the normal distribution cannot be used to approximate the binomial distribution.
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.
As long as the test is two tailed (so that a confidence interval can be used) and since α = .05 and percent confidence = 1 - .05 = .95, then yes, the results will NEARLY ALWAYS be the same between traditional approach and confidence interval approach. Also it will NEARLY ALWAYS be the same between the p-value approach and the confidence interval approach. The reason that I say "almost always" is that the standard error formula for p҄1-p҄2 is slightly different for the confidence interval approach than for the hypothesis testing approach.
The result will ALWAYS be the same between the traditional and p-value approaches whether the test is two tailed or not.
Criteria for rejecting Ho:
Traditional approach: α = .05, reject Ho if z < -1.96 or z > 1.96
P-value approach: Reject Ho if p-value < .05 (which only occurs if z < -1.96 or z > 1.96).
Confidence