Question

ROUND ANSWER TO FOUR DECIMAL PLACES

Determine the upper-tail critical value ta/2 in each of the following circumstances. a. 1-a = 0.90, n = 65 b. 1 - a=0.95, n = 65 C. 1 - a=0.90, n=54 d. 1 - a=0.90, n = 26 e. 1 - a = 0.99, n = 36

Answer 1

a. 1-$\small \alpha$=0.90, n= 65 ;

$\small \alpha$=1-0.90 =0.10 ; $\small \alpha$ /2 =0.10/2 =0.05 ; Degrees of freedom = n-1 = 65-1=64; t$\small \alpha$/2 = t0.05

For 64 degrees of freedom , t0.05 = 1.6690

Answer : 1.6690

b. 1-$\small \alpha$=0.95, n= 65 ;

$\small \alpha$=1-0.95 =0.05 ; $\small \alpha$ /2 =0.05/2 =0.025 ; Degrees of freedom = n-1 = 65-1=64; t$\small \alpha$/2 = t0.025

For 64 degrees of freedom , t0.025 = 1.9977

Answer : 1.9977

c. 1-$\small \alpha$=0.90, n= 54 ;

$\small \alpha$=1-0.90 =0.10 ; $\small \alpha$ /2 =0.10/2 =0.05 ; Degrees of freedom = n-1 = 54-1=53 ; t$\small \alpha$/2 = t0.05

For 53 degrees of freedom , t0.05 =

Answer : 1.6741

d. 1-$\small \alpha$=0.90, n= 26 ;

$\small \alpha$=1-0.90 =0.10 ; $\small \alpha$ /2 =0.10/2 =0.05 ; Degrees of freedom = n-1 = 26-1=25 ; t$\small \alpha$/2 = t0.05

For 25 degrees of freedom , t0.05 = 1.7081

Answer : 1.7081

e. 1-$\small \alpha$=0.99, n= 36 ;

$\small \alpha$=1-0.99 =0.01 ; $\small \alpha$ /2 =0.01/2 =0.005 ; Degrees of freedom = n-1 = 36-1=35 ; t$\small \alpha$/2 = t0.005

For 35 degrees of freedom , t0.005 = 2.7238

Answer : 2.7238