Question

State the critical values for a two-independent-sample t test given the following conditions: a. two-tailed test, α = .01, total df = 26 b. one-tailed test, lower-tail critical, α = .01, df = 15 for each group c. two-tailed test, α = .05, n = 12 in each group d. one-tailed test, upper-tail critical, α = .05, n for both groups combined is 30

Answer 1

Critical values for a t-test are determined by whether it is one-tailed or two-tailed, the significance level, and the degrees of freedom. Without specific tables, estimated critical values for a two-tailed test at α = .01 and df = 26 would be around ±2.779, for a one-tailed test at α = .01 and df = 15 around -2.602, at α = .05 and df = 22 for two-tailed they are about ±2.074, and for a one-tailed test at α = .05 and combined df = 28 it is roughly 1.701.

Step-by-step explanation:

The critical values for a two-independent-sample t-test depend on whether the test is one-tailed or two-tailed, the level of significance (α), and the degrees of freedom (df). Degrees of freedom are usually calculated based on sample size(s) and for two independent samples, the degrees of freedom can be estimated as df = n1 + n2 - 2.

• For a two-tailed test with α = .01 and total df = 26, you would use a t-distribution table, finding the critical value that corresponds to a 0.01 level of significance on each tail, which (usually) totals 0.02. Without the exact table or calculator, we cannot provide the specific value, but it would be around ±2.779 (estimate).
• In a one-tailed test, with the lower-tail critical value at α = .01 and df = 15 for each group, the critical value is found corresponding to the 0.01 level of significance in the lower tail of the t-distribution. This value is typically around -2.602 for df = 30 (however, if df = 15, it would need to be found specifically).
• For a two-tailed test with α = .05 and n = 12 in each group (resulting in df = 22), we would find the critical value from a t-distribution table for a 0.025 level of significance on each tail. This value is approximately ±2.074.
• Lastly, in a one-tailed test with the upper-tail critical value at α = .05, and the n for both groups combined being 30 (making df = 28), you would use a t-distribution table to find the critical value corresponding to 0.05 in the upper tail, which is roughly 1.701.

Remember, exact critical values would need to be computed with the help of statistical software or a t-distribution table that specifically applies to the given degrees of freedom.