*Appropriate Sample Size*

**Appropriate sample size**:

Chadwick (2001) states that if a study is undertaken on an inadequate or inappropriate sample size, then this will influence the accuracy and quality of the results of the study, Piggy Bank should therefore use an appropriate sample in order to reduce costs, time and *still* obtain quality and accurate results.

According to the online journal article by Chadwick (2001) there are number of factors to consider when determining the appropriate sample size, these factors include the margin of error, the primary variable, alpha, the population size and the variance. In this case the margin of error accepted is plus or minus $10, alpha value is 0.02 given that the confidence interval is 98%, and the standard deviation is $500.

The ISIXSIGMA website (2000) an alternative *formula* exists that uses the same concept. This formula according to ISIXSIGMA (2000) is stated as follows = [(T. σ) / E] 2. Where T is the two tail T value at the predetermined alpha value or confidence level, σ is the standard deviation and E is the margin of error.

The confidence level is 98% and the T critical value from the T table is 2.3264, the standard deviation (σ) is given as 500 and the margin of error (E) is given as 10, these values are substituted as follows:

N = [((2.3264)*(500))/10]2

*Appropriate Sample Size*

N= 13530.34

This means that the sample will cost 13530 * $5 = $67651.71

Confidence level when a limitation of $10,000 is put:

The company wants to spend $10,000 on the sample and therefore will be required to reduce the sample size, reducing the sample size will result into an increase in error and inaccurate results. For this reason Piggy bank should consider increasing the margin of error.

The sample

sizethat Piggy bank recommends depends on the cost, the cost is 10,000 and given per sample cost is $5 then the required sample size is 10,000/5 = 2,000

Therefore N = [(T. σ) / E] 2 = 2,000

And that (T. σ) / E= 44.72136

[(2.3264)*(500)]/ E= 44.72136

Therefore E= 26.00994

Therefore if Piggy banks wants to spend 10,000 on the study then the sample size should be

*Appropriate Sample Size*

2,000, however the bank must accept a margin or error amounting to plus or minus $26.00994, it is therefore highly recommended that the bank accepts this margin of error in order to reduce cost.

Pros and cons:

The appropriate sample size given that the standard deviation is 500, confidence interval is 98% and margin of error is $10 is 13530 and this sample will cost $67651.71, this sample will provide more accurate and quality results. However this sample size means that the company will **spend** more. The other option is to spend only 10,000, this case means that the margin of error must be increased from $10 to $26.00994; this means that the confidence interval increases meaning that the results will be less accurate but this sample will cost less. Therefore a larger sample will produce more accurate results but cost more, however a smaller sample size will cost less but provide less accurate results.

References:

ISIXSIGMA (2000) sample size determination, retrieved on 28th February, from http://www.isixs igma.com/library/content/c000709a.asp

OSRA (2001) Organization research: determining sample size, retrieved on 28th February, from www.osra.org/itlpj/bartlettkotrlikhiggins.pdf

STATSOFT (2009) Distribution tables, retrieved on 28th February, from http://www.statsoft.com /textbook/distribution-tables/

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