i. The chi-square goodness-of-fit test can be applied if there are equal or unequal expected frequencies. ii. For a goodness-of-fit test, the following are possible null and alternate hypotheses. Null: Sales are uniformly distributed among the five locations. Alternate: Sales are not uniformly distributed among the five locations.
iii. The number of degrees of freedom appropriate for the chi-square goodness-of-fit test is the number of categories minus 1.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

The chi-square goodness-of-fit test can indeed be applied to both equal and unequal expected frequencies, making statement (i) correct. Statement (ii) accurately represents a common setup for null and alternate hypotheses in a goodness-of-fit test, where the null hypothesis often posits a specific distribution (in this case, uniform distribution across five locations) and the alternate hypothesis suggests a deviation from that distribution. Statement (iii) correctly identifies the formula for calculating degrees of freedom in a chi-square goodness-of-fit test, which is the number of categories minus one. Therefore, all statements (i), (ii), and (iii) are correct.

I the Chi-Square Goodness-Of-Fit Test Can Be Applied If There