Question

A restaurant called Real Ramen recently opened in Staunton, Virginia.  The restaurant offers several types of ramen and ramen-type noodle dishes, designated by the following numbers:  

1 (Tokyo style ramen), 2 (Sapporo style ramen), 3 (Hakata style ramen), 4 (Abura soba),   5 (Maza-men), 6 (Tsuke-men), and 7 (Tantan-men).  

The restaurant’s owners have asked noted University of Virginia professor (and chef) Jim Lark to offer advice regarding restaurant operations.  The owners believe the dishes will be ordered in the following proportions:  1 (25%), 2 (20%), 3(10%), 4 (15%), 5 (5%), 6 (10%), and 7 (15%).  The owners provided the number of orders placed for each dish during the first month of operations: 200 (1), 145 (2), 110 (3), 70 (4), 40 (5), 80 (6), and 105 (7).

Conduct the appropriate hypothesis test to determine whether the owners’ belief regarding the order proportions is correct.  What is the p-value associated with the test statistic?  (If you cannot calculate the p-value, place the best bounds upon the p-value that you can find.)

Answer 1