To find the lower and upper critical values at a 95% confidence level for a sample size of 14, we can use the t-distribution. Since the sample size is 14, the degrees of freedom (df) will be:

$df = n - 1 = 14 - 1 = 13$

For a 95% confidence level, the area in each tail of the t-distribution is $\frac{1 - 0.95}{2} = 0.025$. This corresponds to the critical values that mark the boundaries of the central 95% of the distribution.

Now, we'll find the t-critical values for df = 13 at the 0.025 level in each tail.

Using a t-table or a calculator:

• Lower critical value: $t_{0.025, 13} = -2.160$
• Upper critical value: $t_{0.025, 13} = 2.160$

Thus, the lower and upper critical values are:

• Lower: $-2.160$
• Upper: $2.160$

Would you like further details on how to use the t-distribution table, or have any questions about this?

Additional related questions:

1. How do you calculate the standard error for a t-test?
2. What happens if you use a normal distribution instead of the t-distribution for small sample sizes?
3. How does the confidence level impact the critical values?
4. Why do we use degrees of freedom in the t-distribution?
5. How do you determine the critical values for a different confidence level, like 99%?

Tip: When you’re using the t-distribution, always make sure to use the correct degrees of freedom (df) based on the sample size. This ensures the accuracy of your critical values.