57. 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: B
Chi-square statistic would be used to compare the number of new and used car sales on any given day.
The chi-square statistic is appropriate for comparing categorical data, such as the sales of new versus used cars, particularly when dealing with counts of occurrences in mutually exclusive categories.
A) Z-score
The Z-score measures how many standard deviations an element is from the mean of a dataset. It is primarily used for comparing individual data points within a single distribution rather than comparing two categorical groups, such as new and used car sales.
B) Chi-square
The chi-square statistic is designed for assessing the association between categorical variables. In this context, it allows us to evaluate whether the sales of new cars and used cars differ significantly from expected counts, making it the most suitable choice for comparing the two categories.
C) f-statistic
The f-statistic is used in the context of ANOVA (Analysis of Variance) to compare the variances between groups. This method is not applicable for comparing the counts of new and used car sales, as it does not address the categorical nature of the data.
D) 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 or variables in a regression model. This statistic is not applicable for comparing categorical counts, such as the sales figures for new and used cars.
Conclusion
The chi-square statistic is the most suitable choice for comparing the number of new and used car sales due to its focus on categorical data and the analysis of mutually exclusive groups. Other options like the Z-score, f-statistic, and R-squared do not appropriately address the specific comparison of sales counts between these two categories.