Question

using the z-tables (or t-tables), determine the critical value for the right-tailed z-test with \\( \alpha = 0.10 \\)
options: 2.576, 1.96, 1.282, 2.326, 1.645

Explanation:

Step1: Understand Right-Tailed Test

For a right - tailed z - test with significance level \(\alpha = 0.10\), we need to find the z - value such that the area to the right of this z - value under the standard normal curve is \(\alpha=0.10\). This means the area to the left of the z - value is \(1 - \alpha=1 - 0.10 = 0.90\).

Step2: Use Z - Table

We look up the value in the standard normal (z - table) that corresponds to a cumulative probability of \(0.90\). Looking at the z - table, the z - value corresponding to a cumulative probability of approximately \(0.90\) is \(1.282\) (more precisely, for a cumulative probability of \(0.8997\) we have \(z = 1.28\) and for \(0.9015\) we have \(z = 1.29\), and the value \(1.282\) is a more accurate value for the cumulative probability of \(0.90\)).

Answer:

1.282