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26134 Business Statistics

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Question:

Anna faces a pricing dilemma


Anna is examining prices and wondering where she sits relative to competitors based on when she is open. She only opens for lunch. She does not open for breakfast or dinner.

She thinks that some restaurants charge different prices based on how often they are open during the day (e.g., some open for lunch and dinner), signalling (e.g., a higher price may signal a certain level of quality) and a host of reasons relating to costs etc.

Given a restaurant could open upon three occasions during the day, there are up to seven combinations (23-1) of whether a restaurant serves breakfast, lunch, and/or dinner.

In this question you are asked to calculate and further consider suitable summary statistics for the price of each of these combinations of opening times. To start, calculate the mean price, standard deviation in prices, and number of restaurants (i.e., frequency) for each of the seven combinations.

To help Anna further determine prices being charged by her competitors, you are asked to construct a confidence interval describing the average price of restaurants in each of the seven categories.

Your task is to present these in a nice summary table. That is, construct a table with the seven opening combinations listed in rows and the following columns listed to describe each: average, standard deviation, frequency count, standard error, margin of error, confidence interval lower bound and confidence interval upper bound. Feel free to label the columns using suitable letters (e.g., SD for standard deviation; SE for standard error; n for frequency; ME for margin of error). Add a final row to the table which summarises the average price of those open for lunch regardless of whether they are open for breakfast and/or dinner. Each entry, apart from sample size, should be to two decimal places.

Without doing any formal significance testing (i.e., simply examine your output from above) answer the following:

i) Is there any combination that appears to be significantly more expensive (on average) than any other? Write a short explanation of why this may be the case.
ii) Is there any combination that is significantly less expensive (on average) than any other? Write a short explanation of why this may be the case.
iii) Is there any combination out of the eight possible that does not exist in the sample of restaurants considered? Write a short explanation of why this may be the case.
iv) Explain why some confidence intervals appear to be much wider than others.
v) 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?

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