A researcher is interested in whether frequencies of ice cream preference are evenly distributed across the three categories of vanilla,chocolate,and strawberry.What is the chi-square goodness-of-fit value of the following data?

A)0
B)5.99
C)25.71

Question

A researcher is interested in whether frequencies of ice cream preference are evenly distributed across the three categories of vanilla,chocolate,and strawberry.What is the chi-square goodness-of-fit value of the following data?

A)0 
B)5.99 
C)25.71

Quizplus · Accepted Answer

To calculate the chi-square goodness-of-fit value for this data, we need to compare the observed frequencies (7 for vanilla, 10 for chocolate, and 9 for strawberry) with the expected frequencies if preferences were evenly distributed (8 for each flavor).

The formula for chi-square is Σ(observed-expected)^2/expected.

Plugging in the values, we get:
(7-8)^2/8 + (10-8)^2/8 + (9-8)^2/8 = 0.125 + 0.5 + 0.125 = 0.75

This value is then compared to a chi-square distribution table with 2 degrees of freedom (3 categories - 1 for the expected value). The closest value in the table is 5.99 for a p-value of 0.05.

Since our calculated value (0.75) is smaller than the critical value (5.99), we fail to reject the null hypothesis that the preferences are evenly distributed. Therefore, the best choice is C, and we can conclude that there is no significant difference between the observed frequencies and the expected frequencies if preferences were evenly distributed.

A Researcher Is Interested in Whether Frequencies of Ice Cream