Questions: Using the z table (The Standard Normal Distribution Table), find the critical value (or values) for the right-tailed test with α=0.06. Round to two decimal places, and enter the answers separated by a comma if needed.

Using the z table (The Standard Normal Distribution Table), find the critical value (or values) for the right-tailed test with α=0.06. Round to two decimal places, and enter the answers separated by a comma if needed.

Transcript text: Using the $z$ table (The Standard Normal Distribution Table), find the critical value (or values) for the right-tailed test with $\alpha=0.06$. Round to two decimal places, and enter the answers separated by a comma if needed.

Solution

Solution Steps

Step 1: Determine the Critical Value

To find the critical value for a right-tailed test with significance level $ \alpha = 0.06 $, we need to identify the z-score such that the area to the right of this z-score corresponds to $ \alpha $. This means we are looking for the z-score where the cumulative probability is $ 1 - \alpha = 0.94 $.

Step 2: Calculate the Cumulative Probability

Using the standard normal distribution, we can express the cumulative probability as: \[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(0.94) - \Phi(-\infty) \] Since $ \Phi(-\infty) = 0 $, we have: \[ P = \Phi(0.94) \approx 0.8264 \]

Step 3: Identify the Critical z-Score

The critical z-score corresponding to the cumulative probability of $ 0.94 $ is: \[ Z_{critical} = 0.94 \]