Question

2. You work in the corporate office for a nationwide convenience store franchise that operates nearly 10,000 stores. The per-store daily customer count has been study at 900 for some time (i.e., the mean number of customers in a store per day is 900). To increase the customer count, the corporate office is considering cutting coffee prices. Even with this reduction in price, the franchise will have a 40% gross margin on coffee. To test the new initiative, the franchise has reduced coffee prices in a sample of 34 stores that are randomly chosen. After four weeks of reduced prices, the sample stores stabilize at a mean customer count of 974 and a standard deviation of 96. Is there a way to get a feel for what the mean per-store count in all the stores will be if you cut coffee prices nationwide? Do you think reducing coffee prices is likely to increase mean customer count nationwide? Be specific. Hint:Construct a suitable confidence interval.

Answer 1

In this question, we are given a sample,

size = n = 34

mean = 974

sd = 96

Let us create a 95% confidence interval to check if the mean customer count has increased due reduction in the price.

We are 95% confident that the true population mean for customer count after the price reduction will lie between 941 to 1007

We see that the previous mean of 900 customers is not part of the mean and the confidence interval is higher than 900. Hence we can say that at a significance level of 0.05, the mean number of customer count with the reduction of the coffee price is higher than 900.

Hence we 95% confident that reducing coffee prices is likely to increase mean customer count nationwide