Question 34

A goodness-of-fit test

A goodness-of-fit test is used to determine if the observed counts of votes for contestants significantly differ from the expected counts based on a specific hypothesis. In this case, the test evaluates whether the distribution of votes among the contestants aligns with what would be anticipated.

A) A chi-square test for independence

This test is used to determine if there is a significant association between two categorical variables in a contingency table. It is not appropriate here because the question focuses on the distribution of votes for a single categorical variable (contestants), rather than the relationship between two variables.

B) A chi-square test for homogeneity

A chi-square test for homogeneity is utilized to compare the distribution of a categorical variable across different populations. This option does not apply in this scenario since we are not comparing distributions across multiple groups but rather assessing the fit of observed data against expected counts.

C) A Student's t-test

A Student's t-test is designed for comparing the means of two groups, typically with continuous data. It is not suitable for categorical data or for examining distributions of votes among contestants, which is the focus of the question.

D) A goodness-of-fit test

This test specifically assesses whether the observed frequency counts (in this case, the votes for contestants) fit the expected distribution based on a null hypothesis. Since the question is about evaluating how well the observed data matches expectations, this is indeed the correct test to use.

Conclusion

The goodness-of-fit test is the appropriate choice because it directly addresses whether the observed vote counts for contestants differ significantly from what was expected. Other options, including chi-square tests for independence and homogeneity, as well as the Student's t-test, do not fit the context of assessing a single categorical variable's distribution against expectations.