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1. Give a detailed description of the demographic profile of your sample. The data provided in the various columns will give you ample Information. You need to be organised and determine systematically the types of information that you think would be useful to assist the supermarket chain to make accurate business decisions. Demographic Information such as: average age of your sample; average household income; size of households; marital status, do they live in close proximity to the supermarket; in which zone do the majority of your households live in and what information can you derive about the zones; average yearly purchases; debt levels; proportion of debt to income level, etc., will provide an insight for the business decision makers. Information such as differences in spending habits according to gender; do males generally earn more than females? Do the zone area they live in influence spending habits? (I am sure you can derive more interesting findings!)

2. Explain how the information that you have collected will assist. Provide both numerical and graphic summaries to support your report.

Relation between Household Income and Supermarket Purchases

The present article attempts to identify the description of the income and expenditure of individuals. The research also undertook the effort to identify the relation between household income levels and expenses made in supermarket purchase. The data was categorized on the zone basis; and the influence of the yearly expenditure budget in supermarket purchases was also investigated. The work moreover found the impact of the average yearly spending on increase of spending to improve services in the supermarket (Hunneman, Verhoef, and Sloot, 2015).

Two samples of size 25 each were collected from a population of 1000 individuals. The first sample was selected by Simple Random Sampling (SRS) and the second sample was selected by Stratified Random Sampling (STRS) technique. For STRS, five observations were randomly selected from each zone. The population was balanced between male (N = 484, P = 48.4%) and female (N = 516, P = 51.6%) individuals. The modal value of the age category of the people was centered between 31 and 55 years of age. Zone C was identified as the region with most number of individuals (N = 690, P = 69%), whereas zone E had least number of purchasers (N = 33, P = 3.3%) of products from the supermarkets. Mean of average weekly salaries was found to be $ 73,295.40 (SD = $ 23367.09), and the average yearly expenses was $ 2,387.72.

The SRS sample was obtained by assigning random numbers to each individual observation, and the entire dataset was sorted in ascending order of random numbers. The first 25 sample were selected from the rearranged data set. The STRS sample was first sorted for zones, and then for random numbers in ascending order. The 25 collected samples included first 5 samples from each zone arranged in ascending order. The stratified sample was expected to contain less fluctuation for the continuous variables.

The sample was well balanced between the two genders, with slight skewed towards the males (N = 14, P = 56%) compared to that of the females (N = 11, P = 44%).

Age categories of the individuals were provided instead of exact age, and most of the individuals (N = 12, P = 48%) were found to aged between 31 to 55 years. Eight persons (P = 32%) were aged below 30, and there were five persons (P = 20%) aged above 56 years of age. Hence, the sample seemed to be normally distributed with respected to the age of the individuals.

Sampling Technique: Simple Random Sampling

Average weekly family income of the varied between a range of $ 35,060 to $ 109,290 and the average family income of the sample was calculated as $ 73,782 (SD = $ 20, 732.29). The weekly salary distribution was found to be almost normally distributed with a slight negative skewness. The median weekly average salary was evaluated to be at $ 87,970.

Most of the households (N = 11, P = 44%) did not have any child. nine households (P = 36%) were identified that have one child in their family. Only 5 families (P = 20%) had 2 or more children in their family. Regarding number of total family members, 9 families (P = 36%) were identified to have 3 members in the family. There were 12 households (P = 48%) which had 2 or less members in their family.

In the present sample, 13 people were found to be married (P = 52%) and 12 individuals were (P = 48%) were identified to be unmarried. There was no disproportion in the marital status of the individuals.

Most of the people (N = 15, P = 60%) were found to stay in the proximity of supermarket area.  Other 10 individuals (P = 40%) were found stay at a distance from the supermarkets. Proximity to market areas is supposed to be an influencing factor for additional amount of individual spending.

In the current sample, predominant presence of people from zone C was noted (N = 18, P = 72%). Among the five zones, presence from zone A and E was minor (N = 1, P = 4%), followed by presence from zone D (N= 2, P = 8%) and zone B (N = 3, P = 12%). The inferential results could be influenced by the predominant presence of people from zone C in the sample.

Average yearly purchase of the sample was $ 2521.33 (SD = $ 908.47), where the minimum average yearly expenditure was $ 1359 and the maximum average yearly spending was $ 4856.16. The sampling distribution for average yearly purchase was found to be positively skewed (S = 1.09), and the median yearly expenditure was at $ 2397.26.

Average amount of non mortgage debt of the sample was $ 7451.78 (SD = $ 31176.01), where the minimum average expenditure for consumption goods or services was $ 22,810 and the maximum average expenditure for consumption goods or services was as high as $ 147,980. The sampling distribution for average yearly purchase was found to be normally distributed, and the median expenditure was at $ 90,030.

Sampling Technique: Stratified Random Sampling

People were found to spend 11.2% of their weekly income on an average. The maximum spending was found to be 26.9% of their weekly salary. The distribution for non mortgage debt for the sample was almost normally distributed (S = 0.82), and the median of the debt ratio was found to be at 9.67%.

Males were observed to be better paid than females.  Average salary of males (M = $ 77,487.14) was found to be higher than that of the females (M = $ 69,068.18). The median of weekly average salary was also greater for males (ME = $ 80,045) compare to that of the females (ME = $ 75,040).

Zone D with average yearly spending of $ 3924.24 was identified as the leading zone for average annual expenses, followed by zone C (M = $ 2539.52) and zone E (M = $ 2412). Zone A and B were the two less spending zones. Number of supermarkets could have been a cause for this zone wise average expenditure variation.

The sample was well balanced between the two genders, with distribution of males (N = 13, P = 52%) and the females (N = 12, P = 48%) almost equal.

Similar to SRS sample most of the individuals (N = 12, P = 48%) were found to aged between 31 to 55 years. Eight persons (P = 32%) were aged below 30, and there were five persons (P = 20%) aged above 56 years of age.

Average weekly family income of the varied between a range of $ 31,470 to $ 134, 830 and the average family income of the sample was calculated as $ 78,648 (SD = $ 32,571.19). The weekly salary distribution was found to be negatively skewness. The median weekly average salary was evaluated to be at $ 89,110.

Most of the households (N = 10, P = 40%) did not have any child. Six households (P = 24%) were identified that have one child in their family. 9 families (P = 36%) had 2 or more children in their family. Regarding number of total family members, 19 families (P = 76%) were identified to have 3 or less members in the family.  

In the present stratified sample, 12 people were found to be married (P = 48%) and 13 individuals were (P = 52%) were identified to be unmarried. There was parity in the marital status of the individuals.

Impact of Average Yearly Spending on Supermarket Services

Most of the people (N = 20, P = 80%) were found to stay in the proximity of supermarket area.  Other 5 individuals (P = 20%) were found stay at a distance from the supermarkets.

In the current sample, due to stratified sampling individuals were selected equally (N = 5, P = 20%) from all the zones.

Average yearly purchase of the sample was $ 2778.98 (SD = $ 1260.09), where the minimum average yearly expenditure was $ 1192.6 and the maximum average yearly spending was as high as $ 6709.38. The sampling distribution for average yearly purchase was found to be positively skewed (S = 1.41), and the median yearly expenditure was at $ 2397.26.

Average non mortgage debt of the STRS sample was $ 10,758.38 (SD = $ 4663.20), where the minimum average expenditure was $ 1,133 and the maximum average expenditure for consumption goods or services was as high as $ 20,940. The sampling distribution for average yearly purchase was found to be normally distributed, and the median expenditure was at $ 10,243.2.

People were found to spend 17.25% of their weekly income on an average. The maximum spending was found to be 53.91% of their weekly salary. The distribution for non mortgage debt for the sample was positively skewed (S = 1.46), and the median of the debt ratio was found to be at 15.26%.

Males were observed to be better paid than females.  Average salary of males (M = $ 78,901.54) was found to be slightly higher than that of the females (M = $ 78,375.00). Median weekly average salary for males (ME = $ 94,220) was greater than that of the females (ME = $ 89,110).

Zone E with average yearly spending of $ 3468.85 and zone D  with average yearly spending of $ 3415.12 were the two identified zones for annual expenses, followed by zone C (M = $ 2923.64). Zone A and B were the two less spending zones.

Claim of Management of the Supermarket Chain:

“Significant increase in expenditure towards service improvement was possible for at least $2387 yearly average spending on supermarket purchases”.

The claim of the management of the supermarkets was tested at 5% level of significance by one sample t-test. The average yearly spending was $ 2,521 with a standard deviation of  $ 908.47. The population parameter (average spending) was taken as $ 2387.

Null Hypothesis: H0: : Average yearly spending was at most $ 2387.

Testing the Claim of Management

Alternate Hypothesis: HA: (Right tail test): Average yearly spending was at significantly greater than $ 2387.

Test statistic was calculated as at 24 degrees of freedom. The significance level for right tail was and was greater than. Hence, the null hypothesis failed to get rejected at 5% level, concluding that there was no statistically significant evidence that average yearly expenditure was $ 2387, and there was not enough support to increase expenditure towards service improvement in supermarkets (Campbell, and Stanley, 2015).

The claim of the management of the supermarkets was tested at 5% level of significance by one sample t-test. The average yearly spending was $ 2,779 with a standard deviation of  $ 1,260.09. The population parameter (average spending) was taken as $ 2387.

Null Hypothesis: H0:: Average yearly spending was at most $ 2387

Alternate Hypothesis: HA: (Right tail test): Average yearly spending was at significantly greater than $ 2387.

Test statistic was calculated as at 24 degrees of freedom. The significance level for right tail was and was greater than. Hence, the null hypothesis failed to get rejected at 5% level, concluding that there was no statistically significant inference that average yearly expenditure was $ 2387, and there was not enough evidence to increase expenditure towards service improvement in supermarkets.

Discussion and Conclusion 

The two random sampling techniques yielded samples of 25 each. The zone wise representation of individuals in SRS sampling was insufficient for adequate representation of individuals from each zone. On the contrary, the stratified sample represented five individuals from each zone. The median age in both the samples was around the mid age groups. Gender wise investigation revealed that on average males were earning more than females. The discrepancy in gender wise earning was in line with previous literatures (Apicella, Demiral, and Mollerstrom, 2017; Kitov, and Kitov, 2015). Most of the families were small in size with 2 or less number of members in the households. Zone wise average annual spending for both the samples reflected that zone D individuals were spending more on an average. A one way ANOVA revealed that in simple random sample (F = 2.87, P = 0.138), as well as in stratified sample (F = 2.42, P = 0.082) there was no significant difference in zone wise yearly spending.  

The size of the sample for the present study was not sufficient for significant conclusions. High standard deviations in weekly average salary, annual expenditure, and average non mortgage debts reflected the fluctuation due to random sampling. The size of the sample was not adequate to balance off the fluctuations of the variables. The effect was visible in the inferential analysis, where due to high variation in data values no significant conclusion was obtained. Instead of high average yearly expenditure of certain zones, there was no statistically significant evidence to increase expenditure towards service improvement in supermarkets (Padilla et al., 2015). Neither information about number of supermarkets in different zones was available, nor could the relation of customer average annual expenses and supermarkets’ expenditure towards service improvement be evaluated. The insufficiency in the data also made the sample inadequate for requisite inferential conclusions (Chow, Shao, Wang, and Lokhnygina, 2017).

The two samples differed on the basis of zonal representation, but, no significant difference was noted in terms of decision making by the management of the supermarkets regarding service improvement in the supermarkets.

References 

Apicella, C.L., Demiral, E.E. and Mollerstrom, J., 2017. No gender difference in willingness to compete when competing against self. American Economic Review, 107(5), pp.136-40.

Campbell, D.T. and Stanley, J.C., 2015. Experimental and quasi-experimental designs for research. Ravenio Books.

Chow, S.C., Shao, J., Wang, H. and Lokhnygina, Y., 2017. Sample size calculations in clinical research. Chapman and Hall/CRC.

Hunneman, A., Verhoef, P.C. and Sloot, L.M., 2015. The impact of consumer confidence on store satisfaction and share of wallet formation. Journal of Retailing, 91(3), pp.516-532.

Kitov, I. and Kitov, O., 2015. Gender income disparity in the USA: analysis and dynamic modelling. arXiv preprint arXiv:1510.02752.

Padilla, M., Stehman, S.V., Ramo, R., Corti, D., Hantson, S., Oliva, P., Alonso-Canas, I., Bradley, A.V., Tansey, K., Mota, B. and Pereira, J.M., 2015. Comparing the accuracies of remote sensing global burned area products using stratified random sampling and estimation. Remote sensing of environment, 160, pp.114-121.

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