Sampling
Population and size
Macintosh Inc. has authorized Apple Stores in different locations and the stores around the world themselves are to be treated as the population for this study. Total Apple stores in 19 countries by 2015 were 479. Out of this 268 were in the US itself and 211 in other countries. Thus the total population size for the study is 479.
The Target Population and Rationale
The target populations for this study shall be the Annual store sales for Apple iPad Tablets in terms of the number of units sold for the Fiscal Year ending 2015 and Apple iPhone sales in units sold for the same period . The target population chosen is appropriate for this study as the study intends to investigate a correlation between the sales and this can be objectively arrived at by collecting the sales data from the different stores across the globe. The data is readily available as part of the sales reports of the individual stores and thus can be easily requested and accessed via phone and email. The data is also likely to be accurate and precise being based on the Management reports and information systems, which are usually verified and discussed thoroughly within the companies and there are unlikely to be non-sampling errors present within the data. The study seeks to calculate a correlation coefficient between the two populations samples that of tablet sales and phone sales and see whether there is a negative correlation between the two that is statistically significant.
Sampling Element
The sampling element for the study shall an individual Apple store which shall yield by means of secondary data collected through the sales report a sales figure in terms of number of units sold for the given year as mentioned above.
Sampling Method
Stratified sampling shall be followed. The whole business shall be divided between the US and International Groups or strata.
The reason for the same is that US is the major market for Apple products and the number of stores in US (N=268) itself are more than the combined number of stores in the rest of the world (N=211). Also, US being a different market might have a different trend that is uniquely large enough to study separately.
Sample Size
The sample size as calculated is tabulated below based on the calculations as shown in the Appendix section.
Corrected n for US strata = 158 and for International Strata = 136
Thus total effective sample size for the study is 294.
Data Collection
In order to collect the data, the store managers of each of the stores selected as per the sampling plan shall be contacted simultaneously via email after necessary authorization by the Apple authorities to furnish the data. The email addresses and phone numbers of the store managers shall be collected prior to contacting the managers. This shall be done through the Apple website as well as by contacting the Apple management by apprising them of the purpose and scope of the study. Each of the stores shall sent a formal request asking specifically for the total store sales in units sold, of the Apple iPhone and Apple iPad separately for the fiscal year ending 2015. Each store shall be requested to furnish the information within a span of 48 hours after verifying the written authorization emailed to them along with the data request. Upon receiving the emails from the store managers, the data contained in each of the 294 emails shall be collated and entered in an excel spread sheet and checked for any discrepancies. In case of any apparent discrepancies, the respective store manager shall be contacted to verify the data and if required the discrepancy corrected. In order to protect the data, it shall be stored on a cloud server and password protected.
References
Apple. (2016). Apple Retail Stores. Retrieved July 9, 2016, from www.apple.com: http://www.apple.com/retail/storelist/
Bailar, B. A. (1976). Some Sources of Error and their Effect on Census Statistics. Demography, 273-286.
Greener, S. (2008). Business Research Methods. Ventus Publishing.
Israel, G. D. (1992, November). Determining Sample Size. Retrieved from http://sociology.soc.uoc.gr: http://sociology.soc.uoc.gr/socmedia/papageo/metaptyxiakoi/sample_size/samplesize1.pdf
Teddlie, C., & Yu, F. (2007). Mixed Methods Sampling: A Typology with Examples. Journal of Mixed Methods Research, 77-100.
Appendix: Sample Size Calculations
The sample size is calculated (See Appendix) for mean sample at a confidence level of 95% and 5% margin of error.
The sample size is given by the formula:
n = z2σ2/e2
Where ‘n’ is the sample size, ‘z’ is the coefficient of standard deviation of the sample and is a measure of the distance of an element from the mean in terms of the standard deviation of the sample.
‘σ2’ is the population variance while ‘σ’ is the population standard deviation.
‘e’ is the margin of error.
‘z’ for 95% confidence level is 1.96.
Since the population standard deviation is not known, the standard deviation is assumed to be 0.5 based on a normal distribution to give the largest possible sample size required.
The sample sizes for the US and International markets have been calculated as 384 for both as below.
n = (1.96)2 x (.5)2/ (.05)2=384
Since the population is finite and the sample size is large as compared to the population, the sample size is corrected for finite population and a new sample size is calculated (See Appendix).
The formula for corrected sample size is
Corrected n= n / (1 + (n-1)/N)
Where, N is the size of the finite population.
Thus applying finite population correction for US population,
n US = 384/(1+((268-1)/384)=158
n INTL = 384/(1+((211-1)/384=136
