Question

In a test of$H_0:p=0.4$against $H_a:p\ne 0.4$, a random sample of size 100 yields a standardized test statistic of $z=1.28$. Which of the following is closest to the P-value for this test?

a. 0.90

b. 0.40

c. 0.05

d. 0.20

e. 0.10

Short answer

The correct option is (d) i.e$0.20$

Step-by-step solution

Step 1:Given information

$H_0:p=0.4$

$H_1:p\ne 0.4$

$z=1.28$

Step 2:Calculation

The $P$-value is the probability of getting the value of the test statistic:

$P=P(Z<-1.28\text{or}Z>1.28)$

$=2\times P(Z<-1.28)$

$=0.2006$

$=0.20$

Therefore, the correct option is (d)