Question

1. Customer service delivery time: The Alhambra Restaurant in Ottawa, specializing in ethnic fast food, opened for business just one year ago. It has been a hectic first year for the owner as it often is for small business entrepreneurs in their first 12 months of business. Although the year has been somewhat successful (with the owner averaging $1000 net profit per month after all deductions and expenses), the owner is unhappy with the length of time it has been taking staff to provide customer service (service time at the restaurant is measured from the time the customer enters the restaurant to the moment the customer leaves the counter with their completed food order). The design of all aspects of the restaurant from kitchen layout to placement of service counters was supposed to minimize the time required to serve customers. The restaurant design team was convinced that the restaurant design would permit the owner to achieve an average customer service delivery time of approximately 7 minutes. Given the owner’s concern that the design might not be meeting this objective, the design team commissioned a consultant to conduct a small study examining customer service delivery time. A sample of 20 restaurant customers was selected and the customer service delivery time was recorded to the nearest minute (see table below).                  

5	6	7	10	6	4	7	6	8	5
11	8	7	9	7	8	8	7	9	3

(a) Does the empirical evidence suggest that it takes significantly longer on average to service customers than the 7 minutes anticipated by the design team? Construct a 90% confidence interval estimate of the average customer service delivery time at the Alhambra? Interpret the meaning of this interval in plain, non-technical language (no jargon). Ensure that your non-technical interpretation of these results clearly, concisely, yet comprehensively addresses the owner’s concerns.

(b) Write a brief business report communicating what your consulting team has attempted to do to the head of the Alhambra design team. Remember that the head of the design team does not understand statistical jargon. (One of her staff members does understand statistics and will be looking to ensure that you have conducted a good study, that you have performed a valid analysis of your data, and that your interpretation is appropriate for your study results.) Ensure that your report is thorough, comprehensive, clear, yet concise. Evaluation criteria: quality of writing, clarity, usefulness, comprehensiveness, accuracy, completeness, etc. Attach your typed business report to your assignment.

2. More and more companies in Halifax are trying to enter the lucrative health care products area. Sunray makes a variety of health care appliances for use in the home. One product is a digital blood pressure gauge that can be operated by a patient at home without the aid of a health care professional. Obviously, accuracy of the gauges is important to home users. However, many complaints have been received regarding the accuracy of these gauges. The Canadian Medical Association has jurisdiction over use in Canada of medical devices such as these gauges. Early investigation by a team of association doctors convinced them that the gauges are not functioning accurately. To be fair to the manufacturers of the gauge, the president of the association has decided to conduct a study testing the accuracy of these gauges. Following the typical procedure for testing gauges, the association has selected a group of 15 patients, typical of home users in general. The home users in this study were asked to have their (systolic) blood pressure taken first by an accredited physician (who is assumed to provide accurate readings of systolic pressure) and then, as soon as they got home, by the patients themselves using the Sunray home gauge. The data for the 15 patients tested appears in the table below:

Patient	Physician	Gauge
A	112	126
B	109	108
C	139	116
D	141	123
E	120	138
F	99	123
G	128	119
H	118	122
I	116	116
J	120	118
K	111	114
L	123	108
M	114	130
N	121	123
O	132	127

Do average systolic readings made by patient users of the gauge differ significantly from those taken by physicians? Use a 95% confidence interval (CI) to answer this question. Answer this question using either hand calculations or Excel. If you use an Excel analysis to answer this question, attach the printout of the output to your assignment.

Answer 1

Note : Allowed to solve one question per post.

Solved the second question

Do average systolic readings made by patient users of the gauge differ significantly from those taken by physicians? Use a 95% confidence interval (CI) to answer this question. Answer this question using either hand calculations or Excel. If you use an Excel analysis to answer this question, attach the printout of the output to your assignment.

Put the data in excel as shown.
The formula used as shown below.

We see that the 95% confidence interval is for the mean difference in the measurement of the pressure is -8.03 to 6.96. Since the confidence interval contains zero in it, it is not a statistically valid interval.

Hence we can conclude that there is no sufficient evidence to claim that there is significant different in the measurement systolic readings made by patient users of the gauge and those taken by physicians