Question

Using the t​ tables, software, or a​ calculator, estimate the values asked for in parts​ (a) and​ (b) below.

Answer 1

Answer:

(a) Critical value of t for a 99​% confidence interval with df 26 is 2.48.

(b) Critical value of t for a 98% confidence interval with df 58 is 2.07.

Step-by-step explanation:

We are assuming that both critical values are calculated using the one-tailed test.

(a) We are given the 99% confidence interval with degree of freedom 26.

So, for calculating critical values of t, we need level of significance and degree of freedom;

Degree of freedom for t test = 26

Level of significance = 1 - 0.99 = 0.01 or 1%.

Now, in the t table looking for the critical value at v = 26 and P = 0.01 , we get critical value of t as 2.48.

(b) We are given the 98% confidence interval with degree of freedom 58.

So, for calculating critical values of t, we need level of significance and degree of freedom;

Degree of freedom for t test = 58

Level of significance = 1 - 0.98 = 0.02 or 2%.

Now, in the t table the degree of freedom of 58 is not given, so we have to find the required value between degree of freedom 50 and 60 and P between 5% and 2.5% using interpolation method.

Now, in the t table looking for the critical value at v = 58 and P = 0.02 , we get critical value of t as 2.07.