Need help with this assignment: 1. A national survey was initiated and intended

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Need help with this assignment:

1. A national survey was initiated and intended to capture the prevalence of HIV in the post-HAART (Highly active anti-retroviral therapy) era of treatment. Out of sample of 1,483 participants, a total of 241 were found to be HIV positive.

What is the 95% confidence interval for the proportion who have positive HIV results in the population?

a. 0.1405, 0.1845

b. 0.1437, 0.1813

c. 0.1331, 0.1967

d. 0.1284, 0.1920

2. Suppose a national survey intends to identify the prevalence of Hepatitis C in a population of intravenous drug users. Out of a sample of 6,458 a total of 754 were confirmed to have the disease. What is the 95% confidence interval for the proportion who have Hepatitis C in the population?

a. 0.1070, 0.1266

b. 0.1050, 0.1286

c. 0.1090, 0.1246

d. 0.1109, 0.1227

3. The national blood bank sponsored by the US estimates that approximately 38% of the population has blood type O+. Suppose a local blood bank sampled 140 participants, and determined that 80 participants are O+. We want to test whether the proportion of participants with blood type of O+ in the sample is different from those at the national blood bank using a two-sided one proportion hypothesis test.

Part 1: Our null hypothesis was that the population proportion for those who have blood type O+ in the local blood bank is not different from the national blood bank. What is the 'null value'?

a. 80

b. 140

c. 0.38

d. None of the above

Part 2: What is the standard error of the sample proportion who have blood type of O+ under the assumption that the null hypothesis is true?

a. 0.0518

b. 0.0410

c. 0.0385

d. 0.0557

Part 3: What is the test-statistic (Z-score) for the difference in the proportion of participants with blood type of O+ between the local and national blood banks?

a. 0.1914

b. 3.8511

c. 0.2258

d. 4.6683

Part 4: Using an alpha level of 0.05 and test-statistic calculated in Part 3, what is the correct statistical conclusion?

a. We do have sufficient evidence to reject the null hypothesis.

b. We do not have sufficient evidence to reject the null hypothesis.

c. n/a

d. n/a

4. A research team is hired to investigate the prevalence of periodontal disease in a rural county with a low average socio-economic status. The team is given the task of surveying the area, and providing a brief examination of participants to correctly identify cases of periodontal disease and estimate an overall prevalence. If the team identifiesan overall prevalence of above 25%, the sponsoring organization is to initiate an active campaign promoting healthy dental practice. Out 2,879 participants surveyed, 589 were identified to have periodontal disease. Answer the following.

Part 1: Our null hypothesis was that the population proportion for those who have periodontal disease is different from the threshold set by the sponsoring organization. What is the 'null value' to be compared?

a. 0.25

b. 0.28

c. 589

d. None of the above.

Part 2: What is the standard error of the sample proportion who have perodontal disease under the assumption that the null hypothesis is true?

a. 0.0075

b. 0.0081

c. 0.0089

d. 0.0095

Part 3: What is the test-statistic (Z-score)?

a. -3.55

b. -5.60

c. 2.57

d. 4.19

Part 4: The statistical conclusion was made using an alpha level of 0.05 and test-statistic calculated in Q3 part 3. Then, what would be the action the sponsoring organization will take next step?

a. initiate an active campaign promoting healthy dental practice

b. Do not take further action at this point

c. n/a

d. n/a

5. A comprehensive trial investigating the relationship between vitamin E supplementation and reduced risk for prostate cancer was carried out across the US. Suppose the trial reported that among the 648 patients receiving the supplement program (Group A), 267 developed prostate cancer, while only 212 of the 711 patients without supplementation developed the disease (Group B). We want to test the null hypothesis stating that the proportion of patients who developed prostate cancer is not different between the groups with and without supplement program. Answer the following.

Part 1: What is the difference (Group A- Group B) in the proportion of patients who developed prostate cancer?

a. 0.1138

b. 55

c. 63

d. 0.8730

Part 2: Construct a standard error of the estimate calculated above.

a. 0.0198

b. 0.0201

c. 0.0187

d. 0.0258

Part 3: Calculate the test-statistic (Z-score) and make an appropriate statistical conclusion using an alpha level of 0.05.

a. z-score= 4.4109, we reject the null hypothesis at alpha level of 0.05 (Two-sided)

b. Z-score= -2.840, we failed to reject the null hypothesis at alpha level of 0.05 (Two-sided)

c. Z-score= 3.6091, we reject the null hypothesis at alpha level od 0.05 (Two-sided)

d. Z-score= -4.9080, we failed to reject the null hypothesis at alpha level 0.05 (Two-sided)

I appreciate any work process so I can figure out how to arrive to the answers.

Explanation / Answer

1.

Please 1 question at a time for the assignments:

p = x/n = 241/1483 = .1625

95% CI is given by : p +/- Z*sqrt(p*p'/n)

= .1625 +/- 1.96*sqrt(.1625*.8375/1483)

= .1437 to .1813

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