26134 Business Statistics

Each part will ask you to consider one or more weeks of lecture topic materials. The due date submission will follow at least a week after you have completed a lecture and a tutorial on these particular topics.

Each part of the assignment will contain several questions. The expectation of each question is that you are able to answer the managerial component clearly as well as demonstrate your knowledge in Business Statistics.

In general, the questions will consider your ability to justify your approach (e.g., why did you choose to use the median as a measure of central tendency) and present some information that you obtain using Excel (e.g., a scatter-plot) and reach a managerial conclusion about what you have presented (e.g., should the manager launch the new product based on your analysis?).

In general, the following criteria will be used to evaluate your assignment submission:

o Does it present a clear and well-constructed argument towards the use of this tool, approach or measure? o Does it present inputs into calculations correctly?

o Does it present a justification for the use of these inputs as opposed to alternative inputs?

o Does it present output correctly and accurately? o Is this output easy to understand and read?

o Does it reflect a correct interpretation/conclusion about the output that has been generated?

o Does it avoid the use of unnecessary information and presents a concise answer with a logical flow of ideas?

o Does it communicate an answer in a suitable manner, and is it free from spelling and grammar mistakes?

Question 1) Annabelle faces a location dilemma

Annabelle is examining the various ways in which the locations of restaurants have been described in the database provided. These variables are namely ‘RESTLOC’, ‘CITY123’ and ‘KM2CITY’. She needs some help in terms of what she can and cannot do with each of the three variables with respect to describing the data.

Part i) To further assist, can you create a suitable summary table of sample statistics which describe the central location and spread of the data for each of the three variables describing the location of the restaurants. That is, create a table that has the three variables as column headers and the measures as row headers. The sample mean, sample median, and sample standard deviation should be presented to two decimal places. All other entries should be presented as integers. A possible layout (presented for the cost and cuisine variables to illustrate) could be as follows:

Part ii) To further help her, can you please create a table that describes the measurement properties of the three variables and notes whether each has nominal, ordinal, interval and/or ratio properties as it is presented (i.e., without any further transformation whatsoever).

Here is a possible layout that may be useful as shown for two of the other variables in the database

Part iii) Please revisit the table you presented in Part i, combined with your answer to Part ii). In particular, can you re-present the table, but this time delete those entries that make little sense with respect to providing any meaningful insight for Annabelle. For example, if one had decided a mean cuisine of 5.45 and median cuisine of 5 makes no sense for a manager to consider as relevant or meaningful for any decision or purpose, but a mode of 4 does, one could replace these entries with something to denote this (e.g., n.a. or a hyphen) and re-presenting the first half of the previous table as:

Part iv) Write a short summary describing the location of restaurants based on the analysis of the sample you have been provided and the meaningful statistics you have generated in Part iii.Question 2) Barbara’s concern about parking costs Barbara is working as a planning consultant to the government focused on the location of small businesses. Barbara is particularly interested in examining what the average cost of parking at a parking station that is catering to city-based restaurants (i.e., defined as those restaurants located within 5km of the CBD).

One suggestion from her previous work conducted overseas is that, on average, parking costs should be significantly less than $14 to ensure using a private vehicle to frequent city-based restaurants remains a favourable proposition for potential patrons.

Propose and test a suitable hypothesis to examine this using the sample data provided.

Question 3) Waterviews at a Price Cassie is interested in examining comparable restaurants to her own and wants to explore whether she can justify a premium price based on having waterviews. She is particularly interested in those restaurants that are open for dinner and located in the city. Isolate these restaurants from the sample of restaurants you have been provided and complete the following.

a) Construct a confidence interval that describes the average price charged by citybased restaurants open for dinner with a waterview. Present all your workings and final answer to four decimal places.

b) Construct a confidence interval that describes the average price charged by citybased restaurants open for dinner without a waterview. Present all your workings and final answer to four decimal places.

c) If the confidence intervals do not overlap and the average price of city based restaurants with waterviews open for dinner exceed the average price of city based restaurants without waterviews you should recommend to Cassie that a premium price is justifiable. What would you recommend? Please note, you are not asked to formally hypothesise and test the difference in two means. You are simply asked to construct and compare two confidence intervals.

d) Suppose in step (a) and step (b) that you generated the same sample means and same sample standard deviations in both cases, but hypothetically imagine that these four statistics were based on a sample size of 500 in step (a) and a sample size of 600 in step (b). Describe theoretically what will happen in relation to the confidence intervals if you were to undertake the analysis again.

e) Demonstrate this by repeating steps (a) through (c) with this hypothetical information (i.e., assume the sample size in part a is 500 and 600 in part b). What would you now recommend to Cassie as a result of comparing these newly constructed (hypothetical) confidence intervals?

f) Suggest why Cassie needs to be cautious about whether or not to charge a premium price as you recommend in part (c), based on the analysis you have performed in steps (d) and (e).

Question 4) Family Dinners

John has been arguing with his co-owner that there tends to be fewer restaurants that cater for children and families in the city relative to those outside the city. His co-owner, Danielle argues that it's more about the time of day that the restaurant is open.

To help, Danielle asks you to test whether the occasion upon which the restaurant is open for dinner is independent of whether the restaurant caters for children/families or not. She has asked you to consider this in term of three possible dinner outcomes, categorising restaurants as: i) open exclusively at dinner only; ii) open at dinner, but also at another time of day (i.e., also open at breakfast and/or lunch); or, iii) not open at dinner. Danielle would like you to present several things:

a) A joint frequency table of the three dinner outcomes against whether children/families are catered for or not.

b) A table of expected frequencies of the three dinner outcomes against whether children/families are catered for or not assuming the two events are independent.

c) A table representing your underlying calculations of a chi-square test-statistic to test the independence of the two events of interest.

d) The critical value and a suitable description of how you generated this to conduct your test of independence.

e) A conclusion of what these previous steps inform you with respect to Danielle’s question.

f) Danielle asks you to present three conditional probabilities that illustrate her point. Specifically, determine the probability a restaurant caters for children/families, given the time it is open for dinner as defined above. Danielle also asks you to determine the marginal probability of catering for children/families regardless of opening time.

g) Write a short summary for Danielle and John of what you have determined particularly focused on the outcomes of step (e) and illustrating this point using the outcomes of your calculations from step (f).