Question

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 99.8% confidence interval for the true proportion of all MDS patients on this treatment who will develop leukemia within 5 years of MDS diagnosis.

What is the 99.8% confidence interval? What is the correct interpretation of the confidence interval? Are the assumptions met? Explain.

Conduct a hypothesis test at the 0.05 significance level to test this claim

What are the hypotheses? What is the significance level? What is the value of the test statistic? What is the p-value?

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

What is the appropriate conclusion/interpretation? Are the assumptions met? Explain.

Answer 1

[Used R-Software]

Given is the problem of testing of proportion.

R-commands and outputs:

p0=0.32 # specified population proportion
n=100 # sample size
x=27   
phat=x/n # sample proportion
phat
[1] 0.27
qhat=1-phat
qhat
[1] 0.73

alpha=1-99.8/100 # 99.8% is confidence level
alpha
[1] 0.002

# 99.8% confidence interval

100(1-alpha)% confidence interval is given by:

z=qnorm(1-alpha/2) # Critical value
z
[1] 3.090232
phat-z*sqrt(phat*qhat/n) # Lower limit
[1] 0.1328062
phat+z*sqrt(phat*qhat/n) # Upper limit
[1] 0.4071938

# 99.8% confidence interval is [ 0.1328062, 0.4071938]

######
Condition for one-sample proportion Z-test:
n*p >=10 and n*(1-p) >= 10, where n is the sample size and p denotes proportion.
Yes, the conditions are met.

# Null hypothesis-H0: p=p0 Versus
# Alternative hypothesis-H1: p < p0 (claim)

Test statistic is given by:

z0=(phat-p0)/sqrt(p0*(1-p0)/n) # value of test statistic
z0
[1] -1.071866
pnorm(z0) # p-value
[1] 0.1418901
alpha=0.05 # Significance level
# Here, p-value is greater than alpha, we fail to Reject the null hypothesis H0.

# Correct decision: Fail to Reject the Null Hypothesis
# Conclusion: Result is not significant. There is no enough evidence to conclude that new treatment lead to fewer MDS protocol.