Question

Which is larger (for a 95% confidence interval): the t-stat or the z-stat?

A. a

B. b

C. t

D. z

Answer 1

1) for Z test

the critical value for alpha = 0.05, alpha / 2= 0.05/2 = 0.025

in z stat critical value = Z0.025   = 1.96

2) for t test

for n-1 & alpha/2 = 0.05

let's find the critical value for 0.025 & n-1

i.e   tn-1,0.025 = ?

n	t value
2	4.30
5	2.57
10	2.23
20	2.09
50	2.01
75	1.99
100	1.98
200	1.97

Here for every value of n critical value for t is greater than 1.96( critical value for z )

So we can say that the t score for t is larger than for Z.

Answer:- t