Question

Use the student's t distribution to find tc for a 0.95 confidence level when the sample is 29. (round your answer to three decimal places.)

Answer 1

Using a t distribution table you can easily find the t critical value in a very easy way just look for the confidence level which is 95% or the 5% significance level and look for the degrees of freedom which is 28 (just to remind you degrees of freedom is always -1, so if you have 29 – 1 you will get 28 and it is the degrees of freedom), then the t distribution should give you 2.048 for your t critical value. When you use the significance level here you need to subtract the 100% by your confidence level of 95% you will get the 5% then you should divide it to 2, you will get the .025 if it only a two-tailed test you will use the significance level.

Answer 2

As we are using confidence level. So we are applying a two tailed test.
As given in question confidence level is 0.95.
So two tailed alpha is = 100 - 0.95 = 0.05
One tailed alpha = (two tailed alpha) / 2 =0.05/2 = 0.025

Sample space = 29
So degree of freedom(DF) = N - 1 (Where N = degree of freedom)
So DF = 29 - 1 = 28
So we will use Row DF = 28
Use column alpha = 0.05(two tailed) = 0.025(one tailed.)

So tc for confidence level 0.95 and sample 29 is = 2.048
(from t value chart)