Question

Nationally, 61% of American own American cars, 26% of Americans own Asian cars, and the remaing Americans own non-Asian foreign cars. A survey of 205 people in California finds that 54% own American cars, 31% 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

We can use Chi Square test of Homogeneity to test whether the proportions in California are the same as the national proportions.

For n = 205, the observed frequencies for California are,

O1 = np1 = 205 * 0.54 = 110.7

O2 = np2 = 205 * 0.31 = 63.55

O3 = np3 = 205 * (1 - 0.54 - 0.31) = 30.75

Expected frequencies for whole nation are,

E1 = np1 = 205 * 0.61 = 125.05

E2 = np2 = 205 * 0.26 = 53.3

E3 = np3 = 205 * (1 - 0.61 - 0.26) = 26.65

Chi-Square test statistic, =

= (110.7 - 125.05)² / 125.05 + (63.55 - 53.3)² / 53.3 + (30.75 - 26.65)² / 26.65

=  4.249

=