Question

For the t test , one uses ----------------instead of σ

a. n

b. s

c. χ²

d. t

Using the Z table, find the critical value for

a) α  = .05, two-tailed test

b) α = .01, two tailed test

c) α = .10, two-tailed test

Answer 1

Solution:

Question 1)

is population standard deviation , if it is unknown then we use t test for testing one population mean and we use sample standard deviation s for finding t test statistic.

Thus correct option is: b. s

Question 2)

We have to use z table to find the critical values.

Part a) α  = 0.05, two-tailed test

Since this is two tailed test find α /2 = 0.05 / 2 = 0.025

Look in z table for area = 0.0250 or its closest area and find z value

Area 0.0250 corresponds to -1.9 and 0.06

thus z critical value = -1.96

Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96)

Part b) α = 0.01, two tailed test

Since this is two tailed test find α /2 = 0.01 / 2 = 0.005

Look in z table for area = 0.0050 or its closest area and find z value

Look in z table for Area = 0.0050 and find corresponding z value.

Area 0.0050 is in between 0.0049 and 0.0051, and both the area are at same distance from 0.005

thus we look for both area and find both z values.

Area 0.0049 corresponds to -2.5 and 0.08 , thus z= -2.58

Area 0.0051 corresponds to -2.5 and 0.07 , thus z= -2.57

Thus average of both z values is = ( -2.57 + -2.58 ) / 2 = -2.575

Thus critical z value is = -2.575

Since this is two tailed test , there are two z critical values = ( -2.575 , 2.575 )

Part c) α = 0.10, two-tailed test

Since this is two tailed test find α /2 = 0.10 / 2 = 0.05

Look in z table for area = 0.0500 or its closest area and find z value

Area 0.0500 is in between 0.0495 and 0.0505 and both the area are at same distance from 0.0500

Thus we look for both area and find both z values

Thus Area 0.0495 corresponds to -1.65 and 0.0505 corresponds to -1.64

Thus average of both z values is : ( -1.64+ - 1.65) / 2 = -1.645

Thus Z = -1.645

Since this is two tailed test , there are two z critical values = ( -1.645 , 1.645 )