In: Statistics and Probability
5. Fancy Fish, a fine dining upscale restaurant in Northridge, California and 2016 Open Table Diners’ Choice award winner, is enjoying its eighteenth season of providing delectable food, exceptional service, and beautiful outdoor dining experiences. “Saturday - Half-off Bottled Wine Night” has made Fancy Fish one of the San Fernando Valley’s favorite restaurants. Every Saturday night, guests can enjoy half-off every bottle of wine on the wine list while dining in the restaurant or on the terrace. The owner began offering “Saturday - Half-off Bottled Wine Night” in 2010 as an incentive for guests to dine at Fancy Fish when the economy was in a recession. Now that the economy is booming, the owner is considering whether the promotion should be continued, or even expanded. One concern is the effect that the promotion is having on the overall revenue generated from sales to the participants.
A random sample of 28 checks was collected over the course of one month of Saturday nights. Fourteen checks were from customers participating in the half-off promotion, and the other 14 checks were from customers not participating. The total revenue from each check (less alcohol, tax, and tip) is presented below. Do these data present sufficient evidence that the checks of participants is significantly different from checks of non-participants? What is your recommendation to the owner regarding the status of the promotion?
With Wine Discount W/O Wine Discount
35 46
35 44
36 29
36 29
48 29
29 60
36 64
43 47
24 47
13 49
36 53
50 51
22 44
32 36
Ho : v/s H1 :
Let X be the checks of participants and Y be the checks of non-participants
The critical value of t at level of significance 0.05(two tailed) and 26 ( 14+14-2) degrees of freedom is -2.056
Hence t-value lies in the rejection region. We reject Ho.