Question

Determine the t critical value for a lower or an upper confidence bound in each of the following situations. (Round your answers to three decimal places.)

(a) Confidence level = 95%, df = 10

Answer 1

To find the t-critical value for a one-tailed 95% confidence bound with 10 degrees of freedom, use a t-distribution table or calculator to look up the t-value at the 97.5 percentile, which is approximately 1.812.

Step-by-step explanation:

You are asking about finding the t-critical value for an upper or lower confidence bound when the confidence level is 95%, with degrees of freedom (df) of 10. To find the t-critical value, you may use a t-distribution table or a calculator with statistical functions. If you are looking for a one-tailed test (upper or lower bound), you would typically find the t-value corresponding to 97.5% for a 95% confidence level (since a one-tailed test includes half of the 5% in one tail) and 10 degrees of freedom.

Using the table or a calculator's inverse function for the t-distribution (sometimes noted as 'invT' or 'T.INV'), we can find the t-critical value. For a two-tailed test, you can look up the t-value corresponding to a cumulative area of 0.975 (since 2.5% is in each tail for a 95% confidence interval). However, for a one-tailed test, as you specified for an upper or lower confidence bound, we only use the 97.5 percentile.

The specified critical value for a one-tailed test with df=10 and a 95% confidence level would be approximately 1.812.