Question

A Chi-square test for goodness of fit is used to evaluate preferences for 8 different designs of a new automobile. With a sample of n = 500 the researcher obtained a Chi-square statistic of Chi² = 15.81. What is the correct statistical decision for this outcome (assume p <.05)?

• A. Reject the null hypothesis and conclude that there is no significant difference in preferences.

• B. Reject the null hypothesis and conclude that there is a significant difference in preferences.

• C. Fail to reject the null hypothesis and conclude that there is no significant difference in preferences.

• D. Fail to reject the null hypothesis and conclude that there is a significant difference in preferences.

Answer 1

Null hypothesis: There is no significant difference in preferences.

Alternative hypothesis: There is a significant difference in preferences.

Since we have 8 different designs then degree of freedom of chi square =8-1=7

calculated value of chi square=15.81

alpha=0.05

to find p- value, I will use chi square table

here in row 7(df), we see that 15.81 comes in between 0.025 and 0.05, but it is always less than 0.05

here p- value<0.05, so that we reject the null hypothesis and there is a significant difference in prepferences

option b is correct.