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?

Rationale

Chi-square would be used to compare the number of new and used car sales on any given day.

The Chi-square statistic is ideal for comparing categorical data, such as the mutually exclusive sales of new and used cars. It assesses whether there is a significant difference in the distribution of sales between the two categories.

A (R-squared) YOUR ANSWER

R-squared is a statistical measure that indicates the proportion of variance for a dependent variable that's explained by an independent variable or variables in a regression model. It does not apply to categorical data comparisons and is not suitable for assessing differences in sales between new and used cars.

B (F-statistic) YOUR ANSWER

The F-statistic is used primarily in the context of ANOVA (Analysis of Variance) to compare the means of three or more groups. Since the sales of new and used cars are mutually exclusive and categorical, the F-statistic is not appropriate for this comparison.

C (Chi-square) CORRECT

The Chi-square statistic is specifically designed for testing the independence of categorical variables. In the context of the car dealership, it evaluates whether the frequency of new versus used car sales differs significantly. This makes it the correct choice for comparing the two categories of car sales.

D (Z-score) YOUR ANSWER

The Z-score measures the number of standard deviations a data point is from the mean of a distribution, typically for continuous data. Since the sales figures in this scenario are categorical and mutually exclusive, the Z-score is not applicable for comparing new and used car sales.

Conclusion

When comparing the mutually exclusive sales of new and used cars, the Chi-square statistic is the appropriate choice. It effectively assesses differences in categorical data distributions, making it suitable for analyzing the sales performance of both new and used cars at the dealership. In contrast, the other statistical measures are designed for different types of data and analysis, rendering them ineffective for this specific comparison.

Chi-square would be used to compare the number of new and used car sales on any given day.

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