Question

Use the following information for questions 27-30: A researcher is creating a new treatment protocol for Myelodysplastic Syndrome (MDS), a form of preleukemia.  Following the old treatment protocol, 33% 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.  The researcher decides to conduct the appropriate hypothesis test using α (alpha) = 0.05.  Assume all conditions are met.

Which of the following below best describes the p-value?

	a.	p-value = 0.8997
	b.	p-value = 0.2006
	c.	0.10 < p-value < 0.15
	d.	p-value = 0.1003
	e.	0.20 < p-value < 0.30

Answer 1

Solution :

Given that,

= 0.33

1 - = 0.67

n = 100

x = 27

Level of significance = = 0.0

Point estimate = sample proportion = = x / n = 0.27

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.33

Ha: p < 0.33

Test statistics

z = ( - ) / *(1-) / n

= ( 0.27 - 0.33) / (0.33*0.67) / 100

= -1.28

P-value = P(Z < z )

= P(Z < -1.276)

= 0.1003

c) 0.10 < p-value < 0.15

The p-value is p = 0.1003, and since p = 0.1003 > 0.05, it is concluded that fail to reject the null hypothesis.