Question

Use the following information for questions 1-10: A researcher is creating a new treatment protocol for Myelodysplastic Syndrome (MDS), a form of preleukemia. Following the old treatment protocol, 32% of patients with MDS will develop leukemia within 5 years of MDS diagnosis. He believes his new treatment protocol will lead to fewer MDS patients developing leukemia. He takes a random sample of 100 individuals on his new treatment protocol. Of these 100 individuals, 27 develop leukemia within 5 years of MDS diagnosis. Create a 99% confidence interval for the true proportion of all MDS patients on this treatment who will develop leukemia within 5 years of MDS diagnosis.

1. What is the 99% confidence interval?

2. What is the correct interpretation of the confidence interval from question 1?

3. Are the assumptions met? Explain. Conduct a hypothesis test at the 0.10 significance level to test this claim.

4. What are the hypotheses?

5. What is the significance level? A. 0.01 B. 0.04 C. 0.05 D. 0.10

6. What is the value of the test statistic?

7. What is the p-value?

8. What is the correct decision? A. Reject the Null Hypothesis B. Fail to Reject the Null Hypothesis C. Accept the Null Hypothesis D. Accept the Alternative Hypothesis

9. What is the appropriate conclusion/interpretation?

10.Are the assumptions met? Explain.

Answer 1

1)

sample proportion, = 0.27
sample size, n = 100
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.27 * (1 - 0.27)/100) = 0.0444

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

Margin of Error, ME = zc * SE
ME = 2.58 * 0.0444
ME = 0.1146

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.27 - 2.58 * 0.0444 , 0.27 + 2.58 * 0.0444)
CI = (0.155 , 0.385)

2)

we are 99% confident that the population proportion of all MDS patients on this treatment who will develop leukemia within 5 years of MDS diagnosis is between 0.155 and 0.385

3)

• The sample must be reasonably random
• The sample must be less than 10% of the population
• The sample must be large enough so that:
n• pˆ and n(1 - pˆ ) ≥ 10 for a confidence interval
n• p and n(1 - p) ≥ 10 for the significance test

4)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.32
Alternative Hypothesis, Ha: p < 0.32

5)

0.01 is level

6)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.27 - 0.32)/sqrt(0.32*(1-0.32)/100)
z = -1.07

7)

P-value Approach
P-value = 0.142

8)

As P-value >= 0.01, fail to reject null hypothesis.

9)

There is not sufficient evidence to conclude that new treatment protocol will lead to fewer MDS patients developing leukemia.

10)

• The sample must be reasonably random
• The sample must be less than 10% of the population
• The sample must be large enough so that:
n• pˆ and n(1 - pˆ ) ≥ 10 for a confidence interval
n• p and n(1 - p) ≥ 10 for the significance test