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 test statistic of $z=1.28$. The P-value of the test is approximately equal to

(a) $0.90$.

(b) $0.40$.

(c) $0.05$.

(d) $0.20$.

(e) $0.10$.

Short answer

The correct answer is (d) 0.20.

Step-by-step solution

Given Information

$H_0:p=0.4$

$H_a:p\ne 0.4$

$z=1.28$

Explanation

The $P-$value is the chance of getting the test statistic's result, or a number that is more severe. In table A, find the $P$-value.

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

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

$=2\times 0.1003$

$=0.2006$

$\approx 0.20$