For a confidence level of 80% with a sample size of 22, find the critical t value. Rounding to 3 decimal places is acceptable.

To find the critical t value for a confidence level of 80% with a sample size of 22, follow these steps:

1. Determine the degrees of freedom (df): The degrees of freedom for a t-distribution is calculated as the sample size minus 1. $df = n - 1 = 22 - 1 = 21$

2. Find the alpha level (α): The confidence level is 80%, which means the alpha level is 1 - 0.80 = 0.20. Since the t-distribution is symmetric, we split the alpha level into two tails, so each tail has an area of α/2. $\alpha/2 = 0.20 / 2 = 0.10$

3. Use a t-distribution table or calculator: Look up the t value for 21 degrees of freedom and an area of 0.10 in one tail. This is often denoted as $t_{0.10, 21}$.

Using a t-distribution table or calculator, the critical t value for 21 degrees of freedom and an area of 0.10 in one tail is approximately: $t_{0.10, 21} \approx 1.323$

So, the critical t value is approximately 1.323.