Suppose we are testing the efficacy of a drug to reduce blood pressure. The average blood pressure of women ages 21-30 is 190 mg/dL in the general U.S. population. In a recent study, 100 women were given the new drug and the sample mean blood pressure was measured as 182.73. Assuming the population standard deviation is 35 mg/dL, test the hypothesis that the new drug significantly lowers the blood pressure of women ages 21-30.
1. What are Ho and HA?
a. Ho: μ = 182.73 mg/dL HA: μ # 182.73 mg/dL
b. Ho: µ = 190 mg/dL HA: µ # 190 mg/dL
c. Ho: μ = 182.73 mg/dL HA: μ < 182.73 mg/dL
d. Ho: μ. = 190 mg/dL HA: μ < 190 mg/dL
2. What is the Critical Value? Round to 4 decimal points.
3. What is the Test Statistic? Round to 2 decimal points.
4. Do we reject or fail to reject Ho in favor of HA?
a. Reject Ho in favor of HA as the test statistic is less than the critical value. There is sufficient evidence that the mean blood pressure of those women ages 21-30 taking the new drug is significantly less than the mean blood pressure of women in the same age group.
b. Reject Ho in favor of HA as the test statistic is greater than the critical value. There is sufficient evidence that the mean blood pressure of those women ages 21-30 taking the new drug is significantly less than the mean blood pressure of women in the same age group.
c. Fail to reject Ho in favor of HA as the test statistic is less than the critical value. There is not sufficient evidence that the mean blood pressure of those women ages 21-30 taking the new drug is significantly less than the mean blood pressure of women in the same age group.
d. Fail to reject Ho in favor of HA as the test statistic is greater than the critical value. There is not sufficient evidence that the mean blood pressure of those women ages 21-30 taking the new drug is significantly less than the mean blood pressure of women in the same age group.
5. What is the p-value? In other words, what is Pr(Z < Test Statistic found in Q11)? Round to 4 decimal points.
Construct the two-sided 95% confidence interval for the true population mean blood pressure for the 100 women given the new drug with a sample mean 182.73 mg/dL and standard deviation is 35 mg/dL.
6. The 95% confidence interval for the population mean is (lower bound, upper bound). Round to 2 decimal places.
Suppose you are interested in investigating the factors that affect the prevalence of tuberculosis among intravenous drug users. In a group of 95 individuals who admit to sharing needles, 15 had a positive tuberculin skin test result. The state department of health recently released that the state population proportion of positive tuberculin skin tests is 10%. Test the hypothesis that the sample of intravenous drug users have a higher proportion of positive TB skin tests than the general population with alpha = 0.05.
7. What are the null and alternative hypotheses?
a. Ho: p > po HA: p < po
b. Ho: p = po HA: p ≠ po
c. Ho: p > po HA: p = po
d. Ho: p = po HA: p > po
8. What is the critical value? Round to 4 decimal points.
9. What is the test statistic? Round to 2 decimal points.
10. Is there a significant difference in the proportion of positive tuberculin skin tests among the intravenous drug users and the general population?
a. Reject Ho in favor of HA as the test statistic is less than the critical value. There is sufficient evidence that the prevalence of positive TB skin tests is significantly greater than the general state population.
b. Reject Ho in favor of HA as the test statistic is greater than the critical value. There is sufficient evidence that the prevalence of positive TB skin tests is significantly lower than the general state population.
c. Fail to reject Ho in favor of HA as the test statistic is less than the critical value. There is not sufficient evidence that the prevalence of positive TB skin tests is significantly greater than the general state population.
d. Fail to reject Ho in favor of HA as the test statistic is greater than the critical value. There is not sufficient evidence that the prevalence of positive TB skin tests is significantly lower than the general state population.
11. What is the p-value? In other words, what is the Pr(Z > test statistic found in Q9)? Round to 4 decimal points.
Construct the two-sided 95% confidence interval for the true proportion of positive TB skin tests for intravenous drug users based on the sample of 95 with 15 positive results.
12. The 95% confidence interval for the population proportion is (lower bound, upper bound). Round to 2 decimal places.
Blood-pressure measurements taken on the left and right arms of a person are assumed to be comparable. To test this assumption, 10 volunteers area obtained and systolic blood-pressure readings are taken simultaneously on both arms by the same observer. Note that d' = 2.4 and Σ(di - d-)2 = 654 and use these values as shortcuts to calculating the pooled standard deviation.
|
Patient
|
Right Arm SBP (Group 1)
|
Left Arm SBP (Group 2)
|
|
1
|
125
|
131
|
|
2
|
121
|
124
|
|
3
|
140
|
148
|
|
4
|
101
|
119
|
|
5
|
104
|
99
|
|
Patient
|
Right Arm SBP (Group 1)
|
Left Arm SBP (Group 2)
|
|
6
|
110
|
97
|
|
7
|
123
|
127
|
|
8
|
135
|
138
|
|
9
|
141
|
142
|
|
10
|
159
|
158
|
Use the paired t-test with a significance level of 5% to test whether the left arm reading is significantly higher than the right arm reading.
For easier calculation, define Left Arm SBP as Group 2 and Right Arm SBP as Group 1.
13. What are the null and alternative hypotheses?
a. Ho: The SBP of the left and right arm are equivalent (d = 0) HA: The SBP of the left arm is higher than the SBP of the right arm (d > 0)
b. Ho: The SBP of the left arm is higher than the SBP of the right arm (d > 0) HA: The SBP of the left and right arm are equivalent (d = 0)
c. Ho: The SBP of the left arm is higher than the SBP of the right arm (d > 0) HA: The SBP of the left arm is lower than the SBP of the right arm (d < 0)
d. Ho: The SBP of the left and right arm are equivalent (d = 0) HA: The SBP of the left arm is lower than the SBP of the right arm (d < 0)
14. What is the critical value? Round to 4 decimal places.
15. What is the test statistic? Round to 2 decimal places.
16 Does the left arm SBP significantly read higher than the right arm SBP?
a. Reject Ho in favor of HA because the test statistic falls in the rejection region. There is sufficient evidence that the left arm SBP reading is significantly higher than the right arm SBP reading.
b. Fail to reject Ho because the test statistic falls in the rejection region. There is not sufficient evidence that the left arm SBP reading is significantly higher than the right arm SBP reading.
c. Fail to reject Ho because the test statistic does not fall in the rejection region. There is not sufficient evidence that the left arm SBP reading is significantly higher than the right arm SBP reading.
d. Reject Ho in favor of HA because the test statistic does not fall in the rejection region. There is sufficient evidence that the left arm SBP reading is significantly higher than the right arm SBP reading.
Construct the two-sided 95% confidence interval for true difference in left and right blood pressure readings from the sample of 10 patients with blood pressure readings listed above.
17. The 95% confidence interval for the population mean is (lower bound, upper bound). Round to 2 decimal places.
A study looked at the relationship between alcohol consumption and level of systolic blood pressure (SBP) in women not using oral contraceptives (OC). Alcohol consumption was categorized as follows: no alcohol use; < 10 oz/week alcohol consumption; > 10 oz/week alcohol consumption. The results for the SBP measurements for women 30-39 years of age are given below.
|
Group
|
Mean
|
sd
|
n
|
|
A. No Alcohol Use
|
111.1
|
12.9
|
22
|
|
B. 5_ 10 oz/week alcohol consumption
|
110.4
|
13.4
|
34
|
|
C. > 10 oz/week alcohol consumption
|
115.3
|
14.5
|
10
|
Conduct a two sample independent t-test to determine if women OC users ages 30-39 that consume > 10 oz/week of alcohol (Group 1) have a significantly different SBP than women who consumed no alcohol (Group 2) with an alpha level of 0.05.
18. What are the null and alternative hypotheses?
a. Ho: pi= p.2 HA: µ1 < p.2
b. Ho: p.1 < p.2 HA: p.1 >
c. Ho: µ1 > p.2 HA: p.1 = p2
d. Ho: p1 = p.2 HA: [.11 p2
19. What is the critical value? Round to 4 decimal places.
20. What is the test statistic? Round to 2 decimal places.