Final answer:
The critical t-value for a 95% confidence interval with 19 degrees of freedom can be found using a probability table or a calculator function, such as invT(0.975, 19) on the TI-83, 83+, or 84+. The value 2.093 corresponds to this critical t-value.
Step-by-step explanation:
To find the critical t-value for a 95% confidence interval when dealing with a t-distribution, you can either consult a probability table or use a calculator function. For example, with 19 degrees of freedom, the critical t-value for a 95% two-sided confidence interval is approximately 2.093. This is represented as tα = 2.093.
If you are using a calculator, such as the TI-83, 83+, or 84+, you can use the function invT(0.975, 19) to find this critical value. The 0.975 in the command corresponds to the area to the left of the critical t-value in a two-tailed test, which is required for a 95% confidence interval.
Calculators and computers are convenient tools to calculate critical t-values and other Student's t-probabilities. Remember that for a two-tailed test with a significance level (α) of 0.05 (for 95% confidence), the probability used in the invT function is 1 - α/2 which equals 0.975 for both tails.