Question

Nationally, 60% of American own American cars, 29% of Americans own Asian cars, and the remaing Americans own non-Asian foreign cars. A survey of 212 people in California finds that 53% own American cars, 35% own Asian cars, and the remaining own non-Asian foreign cars. When testing (at the 10% level of significance) whether the proportions in California are the same as the national proportions, what is the test statistic (please round your answer to 3 decimal places)

Answer 1

P( american car | American ) = 0.6
P( Asian car | American ) = 0.29
P( non Asian foreign car | American ) = 1 - 0.6 - 0.29 = 0.11

For the above national percentages, the expected values are computed as:

Expected value for American cars = 212*0.6 = 127.2
Expected value for Asian cars = 212*0.29 = 61.48
Expected value for Asian foreign cars = 212*0.11 = 23.32

The test statistic value here is the chi square test statistic value computed as:

Therefore the test statistic value here is 4.556 ( rounded to 3 decimal places )