56. A car dealership sells both new and used cars. The number of new cars sold on a given day ranges from 5 to 30 while the number of used cars sold ranges from 5 to 40. The number of used cars sold is mutually exclusive to the number of new cars sold. Which statistic would be used to compare the number of new and used car sales on any given day?
Answer: C
Chi-square is the appropriate statistic to compare new and used car sales.
The Chi-square statistic is used to determine if there is a significant difference between the observed frequencies of two categorical variables, in this case, new and used car sales.
A) R-squared
R-squared is a measure used in regression analysis to indicate the proportion of variance in the dependent variable that's predictable from the independent variable(s). It is not suitable for comparing sales figures of new versus used cars, as these are categorical data rather than continuous variables.
B) F-statistic
The F-statistic is typically used in analysis of variance (ANOVA) to compare the variances between different groups. Since the question pertains to categorical counts of sales rather than variances, the F-statistic is not applicable for this comparison.
C) Chi-square
The Chi-square statistic is the correct choice as it is designed to compare the distribution of categorical data. In this context, it can be used to analyze the relationship between the counts of new and used car sales, confirming whether their sales distributions are significantly different.
D) Z-score
The Z-score measures the number of standard deviations an element is from the mean of a set of values. It is used primarily in the context of continuous data and is not appropriate for comparing the counts of discrete categories like new and used car sales.
Conclusion
The Chi-square statistic is the most suitable method for comparing new and used car sales since it directly assesses differences between categorical variables. Other options, such as R-squared, F-statistic, and Z-score, do not fit the requirements for analyzing categorical data in this context, making them inadequate for this specific comparison.