Final answer:
The inconsistency in the serving size of French fries at Frenchies is confirmed by a sample showing a higher standard deviation than the chef's claim. A hypothesis test is needed to statistically verify this discrepancy. In a similar vein, a test of independence can be used to assess whether sales are affected by regional preferences.
Step-by-step explanation:
The concern expressed by the manager of Frenchies about the consistency of French fries servings can be addressed statistically. When the chef claims a standard deviation of at most 1.5 ounces for a 10-ounce order of fries, but the manager suspects it to be higher, an investigation into the variability of the serving sizes is warranted. Upon sampling 49 orders and finding a mean weight of 11 ounces and a standard deviation of 2 ounces, it is clear that the variability is indeed higher than what the chef claims.
To confirm this statistically, one could perform a hypothesis test to see if the observed standard deviation is significantly different from the claimed standard deviation. The sample size, mean, and standard deviation found from the manager's sample would all play crucial roles in this test. Essentially, the goal would be to determine if the observed variability in weight of the fries is greater than what is considered acceptable by the establishment's standards.
In the context of a feasibility study by a major food manufacturer investigating the decline in sales for its skinny fries, a test of independence would be necessary to determine if fries preference is independent of the geographic area. This requires examining the sales distribution in different regions and conducting a statistical test such as a chi-squared test for independence.