Sony would like to test the hypothesis that the average age

Sony would like to test the hypothesis that the average age of a PlayStation user is different from the average age of an Xbox user. A random sample of 32 PlayStation users had an average age of 33.7 years while a random sample of 36 Xbox users had an average age of 35.6 years. Assume that the population standard deviation for the age of PlayStation and Xbox users is 3.7 and 3.5 years, respectively. Sony would like to set = 0.05. The critical value for this hypothesis test would be ________.

Question 28 options:

a. -1.645

b. 2.33

c. ± 1.96

d. 1.28

Solution

Answer : c. +/- 1.96

Key 1 = PlayStation , Key 2 = Xbox

n1 = 32 ; n2 = 36

SD1 = 3.7 ; SD2 = 3.5

Mean1 = 33.7 ; Mean2 = 35.6

dF = ( (SD1)^2/n1 + (SD2)^2/n2 )^2 / (((SD1)^2/n1)^2/(n1-1) + ((SD2)^2/n2)^2/(n2-1))

=( (3.7)^2/32 + (3.5)^2/36 )^2/(((3.7)^2/32)^2/(32-1) + ((3.5)^2/36)^2/(36-1))

= 64.04

alpha = 0.05

This is a two tailed test.

From table ,

Critical value = +/- 1.96