26. 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: A
Chi-square statistic is the appropriate choice for comparing 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 context, it is suitable for comparing the number of new and used car sales, as they are mutually exclusive categories.
A) Chi-square
This option is correct because the Chi-square statistic assesses whether the distribution of categorical data (in this case, new and used car sales) differs from what would be expected under the null hypothesis. Given that new and used car sales are distinct categories, using Chi-square allows for a meaningful comparison of sales performance.
B) R-squared
R-squared is a measure of how well a regression model explains the variability of a dependent variable based on independent variables. It is not appropriate for comparing two mutually exclusive categorical outcomes like new and used car sales, thus making this option incorrect.
C) Z-score
A Z-score indicates how many standard deviations an element is from the mean. While it is useful for understanding individual data points in the context of normal distribution, it does not facilitate the direct comparison of two categorical outcomes. Therefore, this option is not suitable for the given scenario.
D) F-statistic
The F-statistic is typically used in the context of ANOVA to compare variances across groups. Since the question involves comparing two mutually exclusive categories, the F-statistic is not appropriate in this instance, making it an incorrect choice.
Conclusion
The Chi-square statistic is the most appropriate method for comparing the number of new and used car sales, as it effectively evaluates the relationship between two mutually exclusive categorical outcomes. Other options, such as R-squared, Z-score, and F-statistic, do not apply to this context, highlighting why they are incorrect. Thus, the Chi-square statistic stands out as the definitive choice for this analysis.