Question

h₁: p₁ ≠ p₂
identify the test statistic.
z = 1.18
(round to two decimal places as needed.)
identify the p - value.
p - value =
(round to three decimal places as needed.)

Explanation:

Step1: Recognize Test Type

This is a two - tailed z - test (since \(H_1:p_1
eq p_2\)). The test statistic \(z = 1.18\).

Step2: Find P - value for Two - Tailed Test

For a two - tailed test, the P - value is calculated as \(2\times(1 - \Phi(|z|))\), where \(\Phi(z)\) is the cumulative distribution function of the standard normal distribution.
We know that \(z = 1.18\). First, find \(\Phi(1.18)\). Looking up in the standard normal table or using a calculator, \(\Phi(1.18)\approx0.8810\).
Then, \(1-\Phi(1.18)=1 - 0.8810 = 0.1190\).
Multiply by 2 for the two - tailed test: \(P - value=2\times0.1190 = 0.238\).

Answer:

\(0.238\)