The board is very keen to see how we have performed over the last financial year, in order to make sure we are keeping pace with our main competitors. As a result, can you investigate the following?
1. An overall view of gross profit
a. Can you provide me with an overall summary of gross profit?
b. Generally the managers of the top 45 profitable stores across the whole FOODplus supermarket chain are given a bonus for exceptional performance. Based on the survey data, what range of gross profit are we looking at for store managers to receive a bonus this year?
c. I am interested in any store or stores which particularly stand out as being unusual or different in regard to gross profit. Are there any such stores? What do such “unusual” instances mean in statistical terms?
2. Descriptive measures and insights
a. The board wants to revisit the issue of whether it should now be compulsory for our stores to be open every day of the week, including Sunday, in order to be in line with our major competitors. Can you provide a gross profit comparison for our stores that open on Sunday and those that do not?
b. As you know, our latest initiative has been the creation of our online store channel. I know many of our stores have included the online channel as part of their business operations. I have heard that Mall stores are leading the way when it comes to setting up online stores. Is there any evidence of this?
c. Wastage (unsold stock) is expensive to the organisation, especially if maintained at high levels. Can you provide me with an overall breakdown of wastage? I would also be interested in how the States compare when it comes to high levels of wastage in their stores?
3. Significant variation in sales: Other variables
I would like to see whether factors listed below provide any explanation in the variation of Sales between stores. If so, can you also indicate which factor is the most important?
• Advertising expenses
• Number of staff
• Number of car spaces
• Number of trading hours
I realise that the survey relates to a random sample of just 150 of our supermarkets, and that this information can be used to draw inferences about all our FOODplus supermarkets. With that in mind, I hope you are able to provide me with answers to the following questions: 4. Some basic estimates
a. As you know the online store channel is our latest initiative. Can you estimate the average online sales for all supermarkets in the FOODplus chain that have adopted the online channel?
b. Maintaining low wastage levels is naturally the company’s preferred position. To give a better understanding of the situation, can you estimate the proportion of all supermarkets in the FOODplus chain that would be categorised as low wastage? In addition, can you estimate the proportion of FOODplus supermarkets in NSW and Victoria (our two largest markets) that maintain low wastage?
5. Performance: Industry as a whole
a. In a recent report, the Australian Competition and Consumer Commission (ACCC) indicated that the average price increase in a standard basket of food items for a supermarket chain over the last 12 months should be no more than $6.85, which would keep the increase in line with inflation. Is there any evidence to suggest that FOODplus has not complied with the requirements of the ACCC over the last 12 months?
b. We recently received the findings on the independent study we requested into whether all our supermarkets should open on Sunday. The study concluded that 70% of all our supermarkets, at a minimum, have to be open on Sunday in order for FOODplus to remain competitive long term. Is there any evidence to suggest that fewer than 70% of all FOODplus supermarkets currently open on Sunday?
6. Sampling Methods for the Annual Survey
a. I am now thinking more and more that we should have consulted with you before you conducted the survey. I realise the annual survey is based on a simple random sample of 150 stores across the country. But from a perusal of some results I am now concerned about the usefulness of the sample data.
Two things worry me:
i. According to the population number of stores, Queensland appears to be overrepresented in the sample survey while Western Australia and Tasmania appear to be badly under-represented.
Am I correct in my assertion?
ii. I know that the first FOODplus supermarket began operating 27 years ago, yet the maximum age for any supermarket in the sample is 24. Do you have explanation for this anomaly?
b. Finally, I am interested in your opinion about future surveys with regard to performance. In particular, I want to estimate the average gross profit to within $120,000 and the proportion of high
wastage stores to within 6%. Are you able to advise me on the required sample size that satisfies both these criteria?