36. 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
The F-statistic is used to compare the number of new and used car sales on any given day.
The F-statistic is appropriate for comparing the variances between two groups, which in this case are the numbers of new and used cars sold.
A) R-squared
R-squared is a statistical measure that represents the proportion of variance for a dependent variable that's explained by an independent variable in a regression model. It is not suitable for directly comparing the number of new and used car sales since it does not focus on variance between two distinct groups.
B) Z-score
A Z-score measures the number of standard deviations a data point is from the mean of a set of data. While it indicates how unusual a data point is, it does not provide a method for comparing the sales of two different categories like new and used cars.
C) F-statistic
The F-statistic is used to compare the variances between two or more groups. In this scenario, it is the correct statistic to compare the number of new and used car sales, as it helps determine if the differences in sales across these two categories are statistically significant.
D) Chi-square
The Chi-square statistic is used to assess how the observed frequencies in a categorical dataset differ from expected frequencies. While it can be useful for categorical data analysis, it is not the best choice for comparing the numerical sales figures of new versus used cars.
Conclusion
The F-statistic is definitively the right choice for comparing the number of new and used car sales, as it assesses variances between groups. All other options fail to accurately address the comparison needed for the sales data presented, making the F-statistic the most appropriate statistical tool for this analysis.