Q.8 - The Practice of Statistics for AP

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) $0.10$.

Step-by-Step Solution

Answer

The correct answer is (d) 0.20.

Step 1: Given Information

$H_0:p=0.4$

$H_a:p\ne 0.4$

$z=1.28$

Step 2: 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.

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

   $=2\times P(Z<-1.28)$

   $=2\times 0.1003$

   $=0.2006$

   $\approx 0.20$