Question

two - tail z test. test statistic = - 1.79, and \\( \alpha = 0.01 \\).
p - value = \\( \square \\)
(round to four decimal places as needed)
determine whether or not to reject the null hypothesis. choose the correct answer below.
a. reject \\( h _ { 0 } \\), since the p - value is less than the significance level \\( \alpha \\).
b. do not reject \\( h _ { 0 } \\), since the p - value is greater than or equal to the significance level \\( \alpha \\).
c. reject \\( h _ { 0 } \\), since the p - value is greater than or equal to the significance level \\( \alpha \\).
d. do not reject \\( h _ { 0 } \\), since the p - value is less than the significance level \\( \alpha \\).

Explanation:

Step1: Find the p - value for two - tail z - test

For a two - tail z - test, the p - value is calculated as \(2\times P(Z < |z|)\) when \(z\) is the test statistic. Given \(z=- 1.79\), we first find \(P(Z < - 1.79)\) and then multiply by 2.
From the standard normal distribution table, \(P(Z < - 1.79)=0.0367\).
So the p - value \(=2\times0.0367 = 0.0734\)

Step2: Compare p - value with \(\alpha = 0.01\)

We have p - value \(=0.0734\) and \(\alpha=0.01\). Since \(0.0734>0.01\), that is the p - value is greater than the significance level \(\alpha\).
In hypothesis testing, we do not reject the null hypothesis \(H_0\) when the p - value is greater than or equal to the significance level \(\alpha\).

Answer:

p - value: \(0.0734\)
The correct option is B. Do not reject \(H_0\), since the p - value is greater than or equal to the significance level \(\alpha\).