An Overall view of the Gross Profit
Discuss about the Foodmart Supermarkets Business Analysis Report.
This report aimed at determining the minimum, maximum, and the average gross profit for the 150 sampled supermarkets. The report also aimed at determining the level of gross profit made based on different variables such as, number of competitors, hours of trading, location of the store (mall, strip, or country), wages paid among other variables. To determine whether there was significant difference in gross profit based on location of a store, the study revealed there was sufficient evidence to suggest that there was a statistically significant variation in gross profit somewhere across at least two locations (f= 0.436, df= 2, p= 0.648). It was revealed from the analysis that the mean number of competitors FoodMart would expect from the sampled 150 stores would be three competitors. The estimated mean number of competitors per supermarket for all the store would be ± 0.3 of the mean of 3 competitors. As to whether we can estimate the proportion of supermarkets open on Sundays with a 4% significance level, the analysis revealed that the proportion of supermarkets that open on Sundays was 62%. Based on this proportion, at a confidence level of 96% we can say that the supermarkets that open on Sundays will be 62% ± 8.1% that is, they will be between 70.14% and 53.86%. The study found no statistically significant evidence to imply that Foodmart had violated the Australian Competition and Consumer Commission ACCC directive of the mean cost appraisal in a ordinary container for food items for any store chain should be more than $ 6.85 over a period of one year. . The sample size was found to be inadequate based on the formula Cochran (2011) and Fisher (1994) for determining adequate sample size. It is recommended that the survey be done again given that the sample size was inadequate and the sampling procedure was not appropriate.
The first task was to examine the total gross profit made in each state and make a comparison between the states. According to the descriptive statistics, the overall mean gross profit from all the states over the period under review was 1.01 dollars that was associated with a standard deviation of 0.646 dollars. The minimum gross profit was 0.018 dollars while the maximum was 2.872 dollars. The total gross profit realized from the sampled 150 stores was 151.493 dollars. The most common gross profit level (mode) from the sampled stores was 1.512 dollars. The profit range for the top 10% of stores was 0.29 million dollars. That is, the maximum gross profit (2.872 dollars multiply by 10% ) then subtract from the maximum gross profit. This implies that the top 10% of the gross profit of the sampled 150 stores was between 2.872 dollars and 2.58 dollars. Based on the survey data, if the company opts to close five (5) of the least performing stores in terms of gross profit out the sampled 150 stores, the range would be 0.057 million dollars. That is the maximum of five of the least performing store less the minimum gross profit attained from the sampled stores. The estimated gross profit for the group overall according to the analysis was found to be ±0.053 of the sample mean at 95% confidence level. Put another way, it can be said that at 95% confidence level, the gross profit from all the 2,994 stores will be between 0.951 million dollars and 1.063 million dollars based on a sample of 150 stores.
Significant Variation in Gross Profit on a Location Basis
Based on the management’s perception that various locations are more profitable than others, an analysis of variances was carried out. This was to investigate the degree of variances of the gross profit based on the location of a store. The aim of analyzing variation was to establish if the categories of observation are from a similar population. To attain this, comparison is made between the variation of the population means in the categories. Every variation.computes the squared deviation from what would be the expected mean from every population. According to King’oriah (2004), to conduct an ANOVA, various assumptions or conditions had to be met. Namely;
- There are three or more independent groups (locations) that are compared with one another and one quantitative variable (gross profit)
- The sample used is random i.e. the data used is from randomizing a sample of the mean of the population
- The analyzed data is normally distributed
- The is equal variation in the analyzed data within the groups to be compared with one another.
After an assumption has been made on randomization and normal distribution of the data, the task was to determine or test the perception that some locations are more profitable than others are. The null hypothesis for the test was: H0: there is a significant variation in gross profit based on location. The analysis revealed F statistic of .436 that was associated with a p-value of .0648. Since the p-value is greater than 0.05, the null hypothesis (perception of the management) could not be rejected. It was therefore concluded that there was sufficient evidence to suggest that there was a statistically significant variation in gross profit somewhere across at least two locations (f= 0.436, df= 2, p= 0.648).
Upon summarizing the averages of gross profit based on location, stores located in the country had the lowest average gross profit of 0.955 million dollars that was associated with a standard deviation (stdev) from the average of 0.672 million dollars, while the highest average gross profit was recorded in stores located in malls at an average of 1.092 million dollars (stdev= 0.653 million dollars). At the medium were stores located in a strip or shopping centre of a major city at an average of 0.952 million dollars associated with a standard deviation of 0.596 million dollars. However, it would be inappropriate to generalize the performance of each location since there are unequal sample sizes based on the location. Other factors are bound to be attributable to the average gross profit such as population of the inhabitants and accessibility of the stores.
Analyzing the level of competition is an important aspect for any business. In this regard, the estimated mean number of competitors per supermarket was sought. It was revealed from the analysis that the mean number of competitors FoodMart would expect from the sampled 150 stores would be three competitors. Home deliveries for customers’ especially loyal customers are an added incentive to boost sales and eventually increase profit. This is both in terms of convenience to the customers and reliability. The estimated mean number of competitors per supermarket for all the store would be ± 0.3 of the mean of 3 competitors that is, we would be 95% confident that the mean number of competitors would be between 2.7 and 3.3 given a sample of 150 stores.
Some Basic Estimates
As determined from the sampled data a proportion 45 stores that represents 30% of the sampled stores offer home delivery. The question therefore was what proportion of all the Foodmart stores was likely to offer home delivery? The statistical tests carried out revealed that the sample proportion was 5.01% of the total Foodmart stores. The expected proportion of stores that offer home delivery services would be ± 3.5%. Put another way, we can be 95% confident that the proportion of supermarkets that offer home delivery services will be between 8.5% and 1.52% given a sample of 150 stores.
As to whether we can estimate the proportion of supermarkets open on Sundays with a 4% significance level, the analysis revealed that the proportion of supermarkets that open on Sundays was 62%. Based on this proportion, at a confidence level of 96% we can say that the supermarkets that open on Sundays will be 62% ± 8.1% that is, they will be between 70.14% and 53.86%.
To cater for inflation, the Australian Competition and Consumer Commission (ACCC) issued directions that the mean cost appraisal in an normal container for food item for any supermarket chain should be more than $ 6.85 over a period of one year. It was therefore prudent to investigate whether out of the sampled stores the stipulated average price was maintained. The idea was to determine whether there was evidence to imply that Foodmart had not complied with this directive. This was done by investigating whether there was any statistically significant difference between the means of the periods 2015 and 2016 from the mean of $ 6.85. According to the analysis carried out, the results revealed a test statistic of -115.76 that was associated with a p-value of less than .01. It was therefore concluded that there was no statistically significant evidence to imply that Foodmart had violated the ACCC directive.
The annual survey was based on a simple random sample of 150 stores across the country. However, it is not clear the criteria used to come up with the sample of one hundred and fifty. There seems to have been some element of non-probability sampling in particular accidental sampling. The assertion that Queensland is over represented is incorrect as in fact it is New South Wales that is over represented at 39 sampled stores followed by Queensland at 30 stores. It is however correct that Tasmania is among the least represented state at 5 stores sampled while Western Australia is moderately represented at 16 sampled stores.
Your observation that the maximum age for any supermarket from the sample is 24 years of operation is in fact true. However, it is possible that the oldest Foodmart store was not part of the sampled stores. Therefore, this anomaly should be a cause of concern.
The sampled data has helped to answer your concerns thus far. The sample size was found to be inadequate based on the formula Cochran (2011) and Fisher (1994) for determining adequate sample size. The minimum sample size would have been 342 stores based on a target population of 2,994 stores. The appropriate sampling technique that would have been used is stratified proportionate sampling method. This requires obtaining a sample size per stratum from each state since each state has different number of stores. This could have been done by dividing the number of stores per state by the total number of stores then multiplying by the desired sample size. Simple random sample would then have been done at this stage. It is recommended that the survey be done again given that the sample size was inadequate and the sampling procedure was not appropriate.
References and Bibliography
King’oriah, G. K. Fundamentals of Applied Statistics. Nairobi, Kenya: The Jomo Kenyatta Foundation., 2004.
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