The Grocery Market in Australia - Assignment Example

Table of Contents Executive Summary 2 Business Problem 2 Statistical Problem 2 Analysis 3 Answer 1 3 Answer 2 5 Answer 3 6 Answer 4 8 Answer 5 10 Answer 6 12 Conclusion 14 Implications 14 References 15 Executive Summary In 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 Problem There 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 Problem The 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. Analysis Answer 1 Hypothesis: 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 = µ4 Alternate Hypothesis: H1: µ1 ≠ µ2 ≠ µ3 ≠ µ4 Where, µ1 is the average price at Coles/BI-LO µ2 is the average price at Woolworths/Safeway µ3 is the average price at independent stores µ4 is the average price at ALDI Appropriate Test Since, 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. Decision Rule Since there are 4 categories of supermarket, the degrees of freedom between the groups will be (4-1) = 3. Similarly, the degrees of freedom within the groups will be (120-4) = 116. The critical value of F-statistic at 3 df in the numerator and 116 df in denominator with α =0.05 is 2.628. Decision Rule: DO NOT ACCEPT Null Hypothesis if F>2.628 Excel Analysis Source of Variation SS df MS F P-value F crit Between Groups 11840.9938167 3.0000000 3946.9979389 506.6697456 0.0000000 2.6828094 Within Groups 903.6493000 116.0000000 7.7900802 Total 12744.6431167 119.0000000         From the excel output, we know that the calculated value of F for the sample is 506.669. From the figure, we can see that the calculated value is greater than the critical value. The Statistical Conclusion Thus, we can conclude that the Null Hypothesis will NOT be accepted. Business Decision The calculated F-value of 506.67 is much greater than the critical F-value. Moreover the calculated value of p is much less than α =0.05. Therefore there is sufficient evidence suggesting that there is significant difference in the average prices of the four stores. Answer 2 Hypothesis: The Null hypothesis will be the one which assumes that the average price of all the stores across the states is same. The alternate hypothesis will assume that there is significant difference between the average prices of the 3 states. Null Hypothesis: H0: µ1 = µ2 = µ3 Alternate Hypothesis: H1: µ1 ≠ µ2 ≠ µ3 Where, µ1 is the average price at New South Wales µ2 is the average price at Queensland µ3 is the average price at Victoria Appropriate Test Since, we are required to compare the means of 3 categories; the appropriate test that shall be performed is the one-way ANOVA. The Type 5 error rate (α) As it is given, the value of α =0.05. Decision Rule Since there are 3 states, the degrees of freedom between the groups will be (3-1) = 2. Similarly, the degrees of freedom within the groups will be (120-3) = 117. The critical value of F-statistic at 2 df in the numerator and 117 df in denominator with α =0.05 is 3.073. Therefore, we shall not accept the null hypothesis in case the sample F-statistic is greater than 3.073 Decision Rule: DO NOT ACCEPT Null Hypothesis if F>3.073 Excel Analysis The ANOVA table from the Excel Analysis is as shown in the table below: Source of Variation SS df MS F P-value F crit Between Groups 23.11485167 2.00000 11.55742583 0.10629374 0.89924722 3.07376290 Within Groups 12721.52826500 117.00000 108.73101081 Total 12744.64311667 119.00000   From the excel output, we know that the calculated value of F for the sample is 0.1062. From the figure, we can see that the calculated value is lesser than the critical value. The means plot for the four categories of the supermarket is as shown below: Statistical Conclusion Thus, we can conclude that the Null Hypothesis will be accepted. Business Decision The calculated F-value of 0.1063 is lesser than the critical F-value of 3.0737. Moreover the calculated value of p (0.899) is greater than α =0.05. Therefore there is sufficient evidence suggesting that there is no significant difference in the average prices of the four stores. This implies that the market size in the three states is not significantly different. Answer 3 Hypothesis: The Null hypothesis will be the one which assumes that there is no significant difference between the average prices at Woolworth supermarket on two different locations. The alternate hypothesis will assume that there is a significant difference between average prices at Woolworth supermarket on two different locations Null Hypothesis: H0: µ1 = µ2 Alternate Hypothesis: H1: µ1 ≠ µ2 Where, µ1 is the average price at Woolworth supermarket stores located at metropolitan areas. µ2 is the average price at Woolworth supermarket stores located at other locations Appropriate Test The number of samples to be compares is 2. The sample size of 15 is less than 30 and the population standard deviation is not known. Since, the hypothesis is not meant to test if one mean is greater than the other, the correct test shall be two-tailed. Hence the correct statistical test to use is the two tailed t-test. The Type 7 error rate (α) As it is given, the value of α =0.05. Decision Rule The sample size is 15 in each location. Hence the degrees of freedom are 15+15-2 = 28. With 28 degrees of freedom and the type 1 error rate at 0.05, the critical value from the t-table is 2.048. Decision Rule: DO NOT ACCEPT Null Hypothesis if tcalc>3.073 Excel Analysis The table for the equal variances two sample t-test is shown below:   Variable 1 Variable 2 Mean 82.00733333 82.21733333 Variance 8.289778095 2.792206667 Observations 15 15 Pooled Variance 5.540992381 Hypothesized Mean Difference 0 df 28 t Stat -0.244318386 P(T µ2 Where, µ1 is the average price of the staple foods basket at NSW. µ2 is the average price of the staple foods basket at Victoria. Appropriate Test The number of samples to be compares is 2. The sample size of is 40 and the population standard deviation is not known. Since we want to know if one of the means is greater than other, the appropriate test shall be one-tailed. Hence the correct statistical test to use is the one-tailed t-test. The Type 11 error rate (α) As it is given, the value of α =0.05. Decision Rule The sample size is 40 in each location. Hence the degrees of freedom are 40+40-2 = 78. With 78 degrees of freedom and the type 1 error rate at 0.05, the critical value from the t-table is 0.320. Decision Rule: DO NOT ACCEPT Null Hypothesis if tcalc>.0.320 Excel Analysis The table for the equal variances two sample t-test is shown below:   NSW Price Victoria Price Mean 77.013500 78.083250 Variance 98.577069 109.976940 Observations 40.000000 40.000000 Pooled Variance 104.277005 Hypothesized Mean Difference 0.000000 df 78.000000 t Stat -0.468493 P(T.1.6577 Excel Analysis The table for the unequal variances two sample t-test is shown below:   States Price Variable 2 Mean 77.5791667 80.0000000 Variance 107.0978413 0.0000000 Observations 120.0000000 120.0000000 Hypothesized Mean Difference 0.0000000 df 119.0000000 t Stat -2.5625076 P(T Read More