Anna faces a Pricing Dilemma
Anna faces a dilemma of how she should put her prices relative to the numerous competitors in the market. Anna opens only during breakfast and lunch while some of her competitors open for breakfast, lunch and dinner. Furthermore, some only open for breakfast. Some open only for breakfast and lunch like Anna. The major question or rather the dilemma that Anna faces is the best opening hours that will make her at par with her competitors.
Since a restaurant can only open for breakfast, lunch and dinner, there are seven possible combinations of opening hours. That is, a restaurant can open for breakfast only, lunch only, dinner only, breakfast and lunch only, breakfast and dinner only, lunch and dinner only or breakfast, lunch and dinner.
The major task is to find out the best opening time with maximum profit that can make Anna be at par with her competitors. This is going to be done by comparing the prices at the difference combinations of the opening hours. Further, apart from the seven combinations mentioned above, we will also consider the average prices for lunch hours, irrespective of the combination it takes. That is the average for breakfast and lunch, lunch, lunch and dinner and breakfast, lunch and dinner. Therefore, in total, this report is based on eight combinations: breakfast only, lunch only, dinner only, breakfast and lunch only, breakfast and dinner only, lunch and dinner only or breakfast, lunch and dinner and average lunch hour openings. The most important thing is that these are average prices.
The eight combinations mentioned above make up a total of eight variables which are Breakfast, Lunch, Dinner, Breakfast& Lunch, Breakfast and Dinner, Lunch& Dinner, Breakfast, Lunch & Dinner. The other variable derived from the original dataset is COST for2 variable. This variable represents the average prices of the restaurant for two people in $.
To effectively get a solution to the dilemma that Anna faces, we will specifically answer the following questions: Is there any combination that appers to be significantly more expensive (on average) than any other? Is there any combination that is significantly less expensive (on average) than any other? Is there any combination out of the eight possible that does not exist in the sample of restaurants considered? Explain why some confidence intervals appear to be much wider than others. If Anna was to set prices in line with the average charged by her competitors who have similar opening times, what range should her prices be within? How does this range in prices compare to the confidence interval describing the average price of those open for lunch regardless of whether they are known to open for breakfast and/or dinner? These questions are well answered based on the following output of the averages:
|
Column1
|
Column2
|
Column3
|
Column4
|
Column5
|
Column6
|
Column7
|
Confidence interval
|
Column8
|
|
|
Opening Period
|
Mean
|
SD
|
Freq
|
SD Error
|
Margin of Error
|
Lower Bound
|
Upper Bound
|
|
1
|
Breakfast
|
42.10
|
14.37
|
1311
|
0.40
|
0.78
|
41.32
|
42.88
|
|
2
|
Lunch
|
42.10
|
14.37
|
1311
|
0.40
|
0.78
|
41.32
|
42.88
|
|
3
|
Dinner
|
42.12
|
14.37
|
1312
|
0.40
|
0.78
|
41.34
|
42.89
|
|
4
|
Breakfast &Lunch
|
42.10
|
14.37
|
1311
|
0.40
|
0.78
|
41.32
|
42.88
|
|
5
|
Breakfast &Dinner
|
42.05
|
14.37
|
1226
|
0.41
|
0.81
|
41.25
|
42.86
|
|
6
|
Lunch&Dinner
|
42.15
|
14.39
|
1289
|
0.40
|
0.79
|
41.37
|
42.94
|
|
7
|
Breakfast,Lunch&Dinner
|
42.05
|
14.37
|
1226
|
0.41
|
0.81
|
41.25
|
42.86
|
|
8
|
Average Lunch
|
42.10
|
14.38
|
1284
|
0.40
|
0.79
|
41.31
|
42.89
|
From the above output, we can effectively answer the questions at hand. Firstly, it is clear that out of all the possible combinations, there is no combination that averagely appears to be more expensive. The summary table reveals that there only decimal differences (Andrew, 2000). Secondly, we can tell whether there is a combination which appears to be significantly less expensive. From the above table of the output, there is no combination that is significantly less expensive than the other combinations. The average price is $42 with minimal differences in the decimals.
Thirdly, we can tell whether there is any other possible combination that is not mentioned in the eight listed combinations. Since there are only seven possible combinations out of the three opening periods (2^3 -1), only the eight considered combinations are possible (Jean & Christian, 2007).
The fourth questions are an explanation about the reason why some confidence intervals are wider than others. Some confidence intervals are wider than the others due to the sampling errors. This is due to the fact that confidence intervals are computed from the margin of errors. Margin of errors are the variations resulting from sampling errors e. g due to biasedness or making inaccurate entries.
Similarly, another possible reason for the wider range of confidence interval is the nature of the combination being considered. We could say that there is a significant difference in the prices for the breakfast and lunch or breakfast and dinner. We could also say that a combination with three considerations (e.g. breakfast, lunch and dinner) have a wider confidence interval due more room for or cases of sampling errors. Similarly, considering three combinations could be a more room or cases of biasness by the researcher (Andrew, 2000). Moreover, consideration of three combinations could mean more room or cases of incorrect entries. These cases of biasness and sampling errors can be minimised by collecting a sufficiently large enough sample (Jean & Christian, 2007)
The fifth and the last question is an advice to Anna of the best range to set her prices based on the average prices charged by her competitors. Anna should consider setting her prices to match the average prices charged by the competitors. This range of price is indicated in the interval 41.31 (lower bound) and 42.89. Therefore, in order for Ann to keep at par with her competitors, she should set her prices at to be in this range. This will ensure that she sales maximum and get and retain customers.
References
Andrew, W. L. (2000). Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation. Chapman & Hall.
Jean, M. M., & Christian, P. R. (2007). Bayesian Core: A Practical Approach to Computational Bayesian Statistics.
