Question

Critical Values from the t-table (Table D). (a) Accurate to the nearest 3 decimal places, what is the critical value t* that corresponds to the given confidence levels and degrees of freedom?

Answer 1

For a 95% two-sided confidence interval with 19 degrees of freedom, the critical value t* is 2.093 according to the t-table or calculator function invT(0.975, 19).

Step-by-step explanation:

The critical value t* that corresponds to the given confidence levels and degrees of freedom can be found using a t-table or a calculator. Specifically, for a 95 percent two-sided confidence interval and 19 degrees of freedom, the critical value of t is typically found in the row for 19 degrees of freedom and the column corresponding to the desired confidence level. The column for a 95% confidence interval represents an area of 0.025 in each tail of the t-distribution (since it's two-tailed), which is equivalent to a cumulative area of 0.975. The actual value for t* with 19 degrees of freedom for this confidence level is 2.093, according to the information provided.

If we needed to find the critical value for a different degrees of freedom, such as 29, we would look in the same column for the 95% confidence interval and find the intersecting value for the row with 29 degrees of freedom, which would give us the t-score for that setup.