Question

Find the critical value ta/2 needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places.

(a) For level 90% and sample size 8.
(b) For level 99% and sample size 11.
(c) For level 95% and sample size 25.
(d) For level 99.5% and sample size 10.

Answer 1

1.894

3.169

2.064

3.690

Explanation:

A.) 90% ; sample size = 8

Degree of freedom, df = n - 1

t(1 - α/2, 7) = t0.05, 7 = 1.894

B.) 99% ; sample size = 11

Degree of freedom, df = n - 1

t(1 - α/2, 10) = t0.005, 10 = 3.169

C.) 95% ; sample size = 25

Degree of freedom, df = n - 1

t(1 - α/2, 24) = t0.025,24 = 2.064

(D.) 99.5% and sample size 10.

Degree of freedom, df = n - 1

t(1 - α/2, 9) = t0.0025,9 = 3.690