Final answer:
To find the critical t-value for a 95% confidence interval with a sample size of 12, consult a t-distribution table or use a calculator function like invT(0.975, 11) to get the value for 11 degrees of freedom.
Step-by-step explanation:
To find tα/2 when n = 12 for the 95% confidence interval for the mean, we must consider that we have 11 degrees of freedom (since degrees of freedom is n - 1). For a 95% confidence level, the total area in the tails is 5%, so the area in each tail is 2.5%. Using a t-distribution table or calculator, we find invT(0.975, 11), which gives us the desired t-value that corresponds to the 95% confidence level with 11 degrees of freedom.
When finding the t-value for a given confidence interval, you can refer to a probability table or use a calculator function. For a 95% confidence interval with a sample size of 12, the t-value is 2.093. This means that the critical value for the upper and lower bounds of the confidence interval is 2.093.