Question

  1. The owner of a popular chicken restaurant, Chicken-For-Me, with many branches wanted to know if the quality of customer service at a new restaurant was acceptable. One aspect of service that was examined was the length of time that customers had to wait in line before ordering their food. The restaurant decided on acceptable probabilities for the waiting-time categories, and these are given below.
Waiting-time Category
Probability
No more than 1 minute
0.15
More than 1 minute but no more than 3 mins
0.30
More than 3 minutes but no more than 5 mins
0.24
More than 5 minutes but no more than 10 minutes
0.25
More than 10 minutes
0.06
To investigate whether the quality of customer service was acceptable, waiting times were recorded for a random sample of 100 customers at the new Chicken-for-Me. The table below shows the number of customers observed in the five waiting-time categories.
Waiting-time Category
  
Number of Customers
No more than 1 minute
20
More than 1 minute but no more than 3 mins
31
More than 3 minutes but no more than 5 mins
31
More than 5 minutes but no more than 10 minutes
15
More than 10 minutes
3
Total
100
Use the sample data for the 100 customers to conduct a statistical test to determine if the waiting times at the new Chicken-For-Me are inconsistent with the acceptable probabilities for the waiting- time categories.

2.

A randomly selected group of men and women were surveyed to investigate the association between gender and the amount of money spent at a local store, Bullseye. Results are shown in the table below:
Dollars Spent @ “Bullseye”
$0 to $50
$51 to $100
$101 to $200
more than $201
Total
Men
18
85
71
90
264
Women
35
72
98
142
347
Total
53
157
169
232
611
Is there convincing evidence that there is an association between gender and the amount of money spent at “Bullseye”?

Answer 1

1.

No more than 1 minute : Accepted probability = 0.15 i.e. out of 100 customers, 100 x 0.15 = 15 < 20 (Actual result from sample survey)
More than 1 minute but no more than 3 mins : Accepted probability = 0.3 i.e. out of 100 customers, 100 x 0.3 = 30 < 31 (Actual result from sample survey)
More than 3 minutes but no more than 5 mins : Accepted probability = 0.24 i.e. out of 100 customers, 100 x 0.24 = 24 < 31 (Actual result from sample survey)
More than 5 minutes but no more than 10 minutes : Accepted probability = 0.25 i.e. out of 100 customers, 100 x 0.25 = 25 > 15 (Actual result from sample survey)
More than 10 minutes : Accepted probability = 0.06 i.e. out of 100 customers, 100 x 0.06 = 6 > 3 (Actual result from sample survey)

Waiting times were recorded for a random sample of 100 customers at the new Chicken-for-Me.

Thus waiting time is very much within acceptable limit.

2.

There is not enough evidence to conclude. Rather the pattern showing is not regular in nature. Thus there may be a nonlinear relation but that is not clear enough from present evidence.