In a brand awareness study of 80 consumers,52 of them were able to identify "Fusion" as a type of Ford automobile.The chi-square value for a test of this brand awareness was approximately:
A)2.30
B)7.20
C)0.60
D)3.60

Question

Quizplus · Accepted Answer

To calculate the chi-square value for a test of brand awareness, we need to compare the observed number of consumers who identified "Fusion" as a type of Ford automobile with the expected number based on chance.

Assuming that consumers have no prior knowledge or preference for any particular brand, we can use the proportion of Ford automobiles that are Fusions as the expected probability of identifying Fusion correctly. According to Ford's website, Fusion accounts for about 20% of Ford's total sales in the United States. Therefore, we would expect about 16 out of 80 consumers (20% of 80) to correctly identify Fusion by chance.

Using the formula for chi-square, we get:

chi-square = (observed - expected)^2 / expected

For this particular study, the observed number of consumers who identified Fusion correctly was 52, while the expected number based on chance was 16. Plugging these values into the formula, we get:

chi-square = (52 - 16)^2 / 16 = 9.25

Looking up the critical value of chi-square for a significance level of 0.05 and 1 degree of freedom (df = categories - 1), we get:

critical chi-square = 3.84

Since the calculated chi-square value (9.25) is greater than the critical value (3.84), we can reject the null hypothesis that consumers' brand awareness of Fusion is no different from what we would expect by chance. In other words, there is evidence to suggest that consumers have some level of familiarity or recognition of Fusion as a type of Ford automobile.

Therefore, the best choice is B (7.20), which is the closest approximation to the calculated chi-square value of 9.25. Choices A, C, and D are all significantly different from the actual value and can be ruled out.

In a Brand Awareness Study of 80 Consumers,52 of Them