The appropriate statistical procedure to compare the average times of skiers in the two groups (one using one brand of ski wax and the other using a different brand) is the two sample t procedures.
Here's why:
1. Two Sample t Procedures: This method is used when comparing the means of two independent groups to determine if there is a significant difference between them. In this case, the two groups of skiers are independent of each other as they are assigned different brands of ski wax. The two sample t-test allows researchers to assess whether the average times of skiers using one brand of wax differ significantly from those using the other brand.
2. Paired t Procedures: This method is not suitable for this scenario because paired t procedures are used when the same group of subjects is measured twice, under different conditions. In this case, each skier is using a single brand of wax, making them independent samples rather than paired observations.
3. Paired z Procedures: Paired z procedures are similar to paired t procedures but are used when working with large sample sizes and normally distributed data. Since the scenario involves two independent groups of skiers and does not mention large sample sizes or normal distribution assumptions, paired z procedures are not applicable.
4. Two Sample z Procedures: This method assumes that the population standard deviations are known, which is typically not the case in practice. Since ski race times can vary and the standard deviations are not likely known, using two sample z procedures may not be appropriate.
Therefore, the most appropriate statistical procedure for this scenario is the two sample t procedures as it allows for the comparison of the average times of skiers using different brands of ski wax in independent groups.
