Executive SummaryIn order to analyse the state of the grocery market in Australia in 2008, ACCC conducted a survey of the four major supermarkets in the country: Coles/BI-LO, Woolworths/Safeway, Independents and ALDI. The survey collected the prices of the basic staple foods basket at the four stores and classified it according to the state and location. The analysis suggests that there is indeed a significant difference between the 4 stores. The analysis also suggests that the prices do not vary with state and location. However, ALDI has different prices for the three states.
The average price across the three states is $80. Based on the results of the hypothesis tests, it can be said that store managers need to achieve an equitable distribution of stores across states and locations to achieve large economies of scale. With different prices in the three states, ALDI may be loosing on potential higher prices. Business ProblemThere are a lot of assumptions about the grocery market in Australia. One of the assumptions is that markets like the Coles and Woolworths have large economies of scale and hence they have cheaper products as compared to other supermarkets.
It is also argued that different states have different market sizes, and costs resulting in different prices across the states. It is also assumed that the prices differ according to the location of the store. Further, ALDI claims that they have different prices in the three states. It is argued that the prices in NSW are higher than that of Victoria. It is also assumed that the average price of the staple foods basket is higher than $80.
Statistical ProblemThe business problems need to be verified according to the data from the survey conducted by the ACCC. The problems call for hypothesis testing. The first problems require testing if there is significant difference between the average prices of the four stores. It is also needed to test if there is a significant difference between the prices of the 3 states. Similarly, hypothesis testing needs to be done to check if there is between prices of the Woolworths supermarket according to the location and between prices of ALDI stores according to the states.
One-tailed comparison t-test needs to be done to verify if the prices are higher in NSW as compared to Victoria and if the prices across all the four states is greater than 80. AnalysisAnswer 1Hypothesis: The Null hypothesis will be the one which assumes that the average price of all the stores is same. The alternate hypothesis will assume that there is significant difference between the average prices of the 4 supermarkets. Null Hypothesis: H0: µ1 = µ2 = µ3 = µ4Alternate Hypothesis: H1: µ1 ≠ µ2 ≠ µ3 ≠ µ4Where, µ1 is the average price at Coles/BI-LOµ2 is the average price at Woolworths/Safewayµ3 is the average price at independent storesµ4 is the average price at ALDIAppropriate TestSince, we are required to compare the means of 4 samples; the appropriate test that shall be performed is the one-way ANOVA.
The Type 3 error rate (α)As it is given, the value of α =0.05.