Final answer:
To determine if the average purchases at Len's are higher than at Bob's, one needs to perform a hypothesis test such as a t-test or Mann-Whitney U test. The test results, specifically the p-value, will indicate whether there is a statistically significant difference between the two stores' average purchases.
Step-by-step explanation:
The question you've presented appears to be a statistical problem asking whether the average purchases at Len's store exceed those at Bob's. To determine this, one would typically perform a hypothesis test, such as a t-test, if the data is normally distributed, or a non-parametric test like the Mann-Whitney U test if the data does not meet the assumptions of normality.
The aim of these tests would be to compare the means (or medians in the case of non-parametric tests) of the two datasets to see if there is a statistically significant difference.
With the provided data, the null hypothesis (H0) would state that there is no difference in the average purchases between Bob's and Len's stores, while the alternative hypothesis (H1) would suggest that Len's average purchases are higher than Bob's.
After choosing the appropriate test based on the data's characteristics, you would calculate a p-value that indicates the probability of observing the data if the null hypothesis were true. If the p-value is below a predetermined significance level (commonly 0.05), you would reject H0 and conclude that, on average, the purchases at Len's exceed those at Bob's.