Question

For a confidence level of 80% with a sample size of 25, find the critical t value.

Answer 1

To find the critical t value for a confidence level of 80% with a sample size of 25, you can follow these steps:

1. **Determine the degrees of freedom (df)**: This is calculated as the sample size minus 1. For a sample size of 25:
\[
df = n - 1 = 25 - 1 = 24
\]

2. **Determine the critical value for the t-distribution**: Since the confidence level is 80%, the remaining percentage in the two tails of the distribution is \(100\% - 80\% = 20\%\). Since it is a two-tailed test, you will need to divide this by 2:
\[
\alpha = \frac{20\%}{2} = 10\% = 0.10
\]

3. **Look up the critical t value**: You can use a t-distribution table or statistical software to find the critical t value for \(df = 24\) at a significance level of \(0.10\) for each tail.

If you look it up in a t-table for \(df = 24\):
- The critical t value at a significance level of \(0.10\) in each tail (for a two-tailed test) is approximately \(t_{0.10, 24} \approx 1.318\).

Thus, the critical t value for a confidence level of 80% with a sample size of 25 is approximately ±1.318.