Task 1
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.
Response:
Set up the null and alternative hypothesis which are:
Ho: P1 = P2
Ho: P1 ≠ P2
P1 is the proportion of men and P2 is the proportion of women. Level of significance is α = 0.05
These methods yield the same conclusion
Under P-value method, p-value is less than α = 0.05, we reject Ho, otherwise not.
Under traditional method, the test statistic value is less than the critical value, we reject Ho, otherwise not.
Under the confidence interval method, the confidence interval contains 0, we reject Ho, otherwise not.
Task 2
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, unless your instructor stipulates otherwise.
H_0= The unfiltered king-size cigarettes have a mean tar content greater than that of filtered 100 mm cigarettes.
a. Use a 0.05 significance level to test the claim that unfiltered king-size cigarettes have a mean tar content greater than that of filtered 100 mm cigarettes.
|
Sample
|
N
|
Mean
|
Standard Deviation
|
SE Mean
|
|
1
|
25
|
21.1
|
3.2
|
6.4
|
|
2
|
25
|
13.2
|
3.70
|
0.74
|
The difference between the two is 7.90000
b. What does the result suggest about the effectiveness of cigarette filters?
As we can see above we can clearly see that the 100 mm filtered cigarettes have less than unfiltered king size cigarettes. This shows us that filters are more effective on cigarettes than unfiltered cigarettes alone.
2. 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
|
0.05 To claim that there is a difference. L3= L1-L2≠0
H0 = 0
H1 ≠ 0