Question

using the z table (the standard normal distribution table), find the critical value (or values) for the left - tailed test with α = 0.09. round to two decimal places, and enter the answers separated by a comma if needed.
critical value(s):

Explanation:

Step1: Recall the property of left - tailed test

For a left - tailed test with significance level $\alpha$, we need to find the \(z\) - value \(z_{\alpha}\) such that \(P(Z<z_{\alpha})=\alpha\). Here \(\alpha = 0.09\).

Step2: Use the standard normal distribution table

We look for the value in the body of the standard normal distribution table (the \(z\) - table) that is closest to \(0.09\).
The standard normal distribution table gives the cumulative probability \(P(Z < z)\).
Looking up the value in the \(z\) - table:
The cumulative probability \(P(Z < z)=0.09\).
We know that for \(z=-1.34\), \(P(Z < - 1.34)=0.0901\) (using the standard normal table: the row for \(z=-1.3\) and the column for \(0.04\): \((-1.3)+0.04=-1.34\)).
Since \(0.0901\) is very close to \(0.09\) (and we are asked to round to two decimal places), the critical value for the left - tailed test with \(\alpha = 0.09\) is \(z=-1.34\).

Answer:

$-1.34$