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.

What is the Value of the Test Statistic?

a. -1.35

b. 1.35

c. -1.28

d. 1.28

e. -2.71

Answer 1

Solution :

Given that,

= 0.33

1 - = 0.67

n = 100

x = 27

Level of significance = = 0.05

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

Option c is correct.

Critical value of  the significance level is α = 0.05, and the critical value for a left-tailed test is

= -1.64

P-value = P(Z < z)

= P(Z < -1.28)

= 0.1003

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