Suppose we are testing the efficacy of a drug to reduce blood pressure. In a recent study, 100 women were given the new drug and the sample mean blood pressure was measured as 182.73 mg/dL. Generate a 95% confidence interval (lower bound, upper bound) for the true mean blood pressure in women who use the new blood pressure reduction drug. Assume the population standard deviation (σ) is known to be 35 mg/dL.
Question 1. The lower bound of the 95% confidence interval is
a. 182.04
b. 176.97
c. 175.87
d. 189.59
Question 2. The upper bound of the 95% confidence interval is
a. 189.59
b. 183.42
c. 188.49
d. 176.97
Suppose we know the true average blood pressure of women ages 21-30 is 190 mg/dL in the general U.S. population. Using the sample information provided in questions 1 and 2, test the hypothesis that the new drug significantly lowers the blood pressure of women ages 21-30.
Question 3. What are H0 and HA?
a. H0: µ = 182.73 mg/dL; HA: µ ≠ 182.73 mg/dL
b. H0: µ = 190 mg/dL; HA: µ ≠ 190 mg/dL
c. H0: µ = 182.73 mg/dL; HA: µ < 182.73 mg/dL
d. H0: µ = 190 mg/dL; HA: µ < 190 mg/dL
Question 4. What is the Critical Value?
a. Z = -1.96
b. Z = 1.96
c. Z = 1.645
d. Z = -1.645
Question 5. What is the Test Statistic rounding to two decimal places?
a. -2.08
b. 2.08
c. 182.73
d. -1.83
Question 6. True or False: We reject the null hypothesis in favor of the alternative.
Question 7. What is the p-value of the test statistic calculated in question 5? Round to 4 decimal points.
a. 0.9812
b. 0.0188
c. 0.0287
d. 0.9713
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, 19 had a positive tuberculin skin test result. Generate a 90% confidence interval (lower bound, upper bound) for the percent of positive tuberculin skin test result.
Question 8. The lower bound of the 90% confidence interval is
a. 0.73
b. 0.20
c. 0.27
d. 0.13
Question 9. The upper bound of the 90% confidence interval is
a. 0.80
b. 0.27
c. 0.87
d. 0.20
The state department of health recently released that the state population proportion of positive tuberculin skin tests is 16%. Using the sample information from questions 8 and 9, 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. Round all intermediate calculations to 4 decimal places.
Question 10. What are the null and alternative hypotheses?
a. H0: p > p0; HA: p < p0
b. H0: p = p0; HA: p ≠ p0
c. H0: p > p0; HA: p = p0
d. H0: p = p0; HA: p > p0
Question 11. What is the critical value? Round to 4 decimal points.
a. Z = -1.96
b. Z = 1.96
c. Z = 1.645
d. Z = -1.645
Question 12. What is the test statistic? Round final answer to 2 decimal points.
a. 1.07
b. 10.37
c. -1.07
d. -10.37
Question 13. Is there a significant difference in the proportion of positive tuberculin skin tests among the intravenous drug users and the general population?
a. Reject H0 in favor of HA as the test statistic is less than the critical value.
b. Reject H0 in favor of HA as the test statistic is greater than the critical value.
c. Fail to reject H0 in favor of HA as the test statistic is less than the critical value.
d. Fail to reject H0 in favor of HA as the test statistic is greater than the critical value
Question 14. What is the p-value of the test statistic calculated in question 10? Round to 4 decimal places.
a. 0.1423
b. 0.8577
c. 0.9999
d. 0.0001
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 Xd¯ = d¯ = 2.4 and ∑(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)
|
|
Patient
|
Right Arm SBP (Group 1)
|
Left Arm SBP (Group 2)
|
|
1
|
125
|
131
|
6
|
110
|
97
|
|
2
|
121
|
124
|
7
|
123
|
127
|
|
3
|
140
|
148
|
8
|
135
|
138
|
|
4
|
101
|
119
|
9
|
141
|
142
|
|
5
|
104
|
99
|
10
|
159
|
158
|
Use the paired t-test with a significance level of 5% to test whether the left arm reading is significantly different than the right arm reading. For easier calculation, define Left Arm SBP as Group 2 and Right Arm SBP as Group 1. Round all intermediate calculations to 4 decimal places.
Question 15. What are the null and alternative hypotheses?
a. H0: 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. H0: 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. H0: 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. H0: The SBP of the left and right arm are equivalent (d = 0)
HA: The SBP of the left arm is different than the SBP of the right arm (d ≠ 0)
Question 16. What is the critical value? Round to 4 decimal places.
a. t = 1.8331
b. t = 2.2622
c. t = 1.7291
d. t = 2.0930
Question 17. What is the test statistic? Round final answer to 1 decimal place.
a. 0.7
b. 0.8
c. 0.9
d. 1
Question 18. True or False: Reject the null hypothesis in favor of the alternative.
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
|
var
|
n
|
|
A. No Alcohol Use
|
105.3
|
10.6
|
24
|
|
B. ≤ 10 oz/week alcohol consumption
|
110.4
|
13.4
|
22
|
|
C. > 10 oz/week alcohol consumption
|
122.5
|
12.5
|
10
|
Conduct a two sample independent t-test to determine if women OC users ages 30-39 that consume > 10 oz/week of alcohol (define as Group 1) have a significantly higher SBP than women who consumed no alcohol (define as Group 2) with an alpha level of 0.05. The pooled standard deviation s is 3.34.
Question 19. What are the null and alternative hypotheses?
a. H0: μ1= μ2; HA: μ1 > μ2
b. H0: μ1 < μ2; HA: μ1 > μ2
c. H0: μ1 > μ2; HA: μ1 = μ2
d. H0: μ1 = μ2; HA: μ1 < μ2
Question 20. What is the critical value? Round to 4 decimal places.
a. t = 2.622
b. t = 1.96
c. t = 1.645
d. t = 1.6939
Question 21. What is the test statistic? Round to 2 decimal places.
a. 30.03
b. 10.73
c. 5.56
d. 13.68
Question 22. Do women that consume > 10 oz/week of alcohol have significantly greater SBP than those who do not consume any alcohol?
a. Fail to reject H0 because the test statistic is greater than the critical value.
b. Fail to reject H0 because the test statistic is less than the critical value.
c. Reject H0 in favor of HA because the test statistic is greater than the critical value.
d. Reject H0 in favor of HA because the test statistic is less than the critical value.