Question

Which of the following is an accurate comparison between the expected and observed frequencies for a chi-square test?

a. Observed frequencies can contain negative values, and expected frequencies are always positive values.
b. Expected frequencies can contain fractions or decimal values, and observed frequencies are always whole numbers.
c. Observed frequencies can contain fractions or decimal values, and expected frequencies are always whole numbers.
d. Expected frequencies can contain negative values, and observed frequencies are always positive values

Answer 1

Answer:

The correct answer is b. Expected frequencies can contain fractions or decimal values, and observed frequencies are always whole numbers.

In a chi-square test, expected frequencies are calculated based on the null hypothesis, assuming a specific distribution or relationship between variables. These expected frequencies can take on fractional or decimal values, as they are calculated using probabilities or mathematical models.

On the other hand, observed frequencies are the actual counts or frequencies observed in the data. Since they are based on real observations or measurements, they are always whole numbers.

Option a is incorrect because observed frequencies cannot be negative values. Option c is also incorrect because both observed and expected frequencies can contain fractions or decimal values. Option d is incorrect because expected frequencies cannot be negative values.