Descriptive Statistics

Sampling Design:

Independent Variable

The independent variable is the database used and advice given to the customers. The database used is either more or less proficient, and the advice given is either useful or obsolete.

Dependent Variable

The dependent variable is the length of the turnaround time for the stock data, and the customers' profit. The dependent variable is dependent on the turnaround time for the stock data.

Research Question

The sample size used in this study is sufficient, given the analysis shown in the appendix, as it is well above the recommended sample size obtained from a 95% confidence interval and a 5% margin of error.

The database used and advice given to the customers will be determined through the length of the turnaround time for the stock data and the customers' profit. While choosing a particular month may make the analysis easier, using the entire year will avoid inconsistencies between databases that advice customers in peak season. Utilizing, the entire year, should help standardize for location-based customer dynamics, and will similarly increase the accuracy and credibility of the study. The data will physically be obtained by requesting customers about their experience.

After the data is collected and obtained, it will be stored on a secure computer and will be shared amongst the researchers. Great care will be taken to ensure Trifold Investment Group, and the researchers will ensure the data is not made available inadvertently to parties who are not involved in the research. Utmost care will be taken to ensure the data is not lost or tampered with, and proper research integrity is maintained. A fortunate aspect of this study will be the lack of risk involved with human subjects or customers. There will be no adverse effect on Trifold Investment Group consumers by the implementation of this research, so there should be little hesitation on Trifold’s part to cooperate with the researchers.

Overall, this study will aim to determine if, in fact, there is a relationship between the presence of advice and time Trifold Investment Group. The null hypothesis of this study will be that the sample mean of advice delivered to customers do not have significant relationship with length of the turnaround time for the stock data, and the customers' profit, (μ_1), will be the same as the sample mean of advice delivered to customers do have significant relationship with length of the turnaround time for the stock data, and the customers' profit, (μ_2).

〖Hyptoheses to be tested: H〗_(o: ) μ_1=μ_2 , H_(a: ) μ_1≠μ_2

As mentioned before, reliability of this study will be obtained by using a sample size larger than the recommended sample size given a 95% confidence interval and 5% margin of error. Additionally, the sample mean will represent advice to customers during the entire year to standardize for location specific customer dynamics. Validity of the study will be achieved by ensuring that a SRS is utilized to collect the data, and the integrity of the data does not become compromised. Special care will be taken to ensure the data is secured, and all statistical work be done accurately. Special care will be taken to ensure that all statistical estimates are valid. For instance, the recommended sample mean, is shown to be a valid estimate and the confidence interval a valid indicator of the sample mean, given the fulfillment of the criteria discussed in Appendix 1. Overall, this experimental design will be made reliable and valid not only through the collection of proper data but the high effective work of the researchers performing this study

Appendix 1:

Recommended Sample Size for 95% CI and 5% ME:

Note: In order to calculate a sample size, we would need to have an idea about the standard deviation in advice, which is data we do not have, prior to carrying out this study. However, an alternative approach we can use is to use the proportion of customers consulting for advice in units to calculate our recommended sample size.

ME=z√((p ̂ )(1-p ̂ )/n) , solving for n yields: n=〖(z/ME)〗^2 (p ̂ )(1-p ̂ )

See References 2-4 for more info:

Now, we are given ME=.05, the z-score corresponding to a 95 Confidence Interval 1.96, and the proportion of stores having store front recycling units will need to be determined.

The proportion of customers who consult for advice was 5% in 2011 since then Trifold has claimed at most a 67% per year increase in 2013 (1). It can be assumed the percentage was less than that on average per year over the last three years (1). In order to achieve the most accurate sample size, we should assume that the increase per year was 67% (2, 3, and 4). This will maximize the denominator in the equation shown below, thus producing a sample size that overcompensates for or lack of an accurate statistic, and will still therefore be reliable (2, 3, and 4).

p ̂=(5%)(1.67)(2014-2011)=(23.29%), therefore the sample size will be:

n=〖(z/ME)〗^2 (p ̂ )(1-p ̂ )=〖(1.96/(.05))〗^2 (.23)(1-.23)=272.14

See References 2-4 for more info:

This estimate can be considered reasonably accurate because:

The sample is a SRS and was obtained from a binomial population ( (2, 3, and 4)!

Both np ̂≥10 and np ̂(1-p ̂)≥10 (2, 3, and 4).

The size of the population (23,000+) is at least ten times the size of the sample, n (2, 3, and 4).

*Therefore, we can assume that if our sample size is greater than 272.14, our study will produce reliable results (2, 3, and 4).

References:

1. Recycling & Reducing Waste| Starbucks Coffee Company | Starbucks Coffee Company. (n.d.). Retrieved July 31, 2014, from http://www.starbucks.com/responsibility/environment/recycling

2. Hypothesis Testing of the Difference Between Two Population Means. (n.d.). Retrieved July 31, 2014, from http://www.kean.edu/~fosborne/bstat/07b2means.html

3. Statistics Notes Class 23: Retrieved July 31, 2014, from http://www.unc.edu/~rls/s151-2010/class23.pdf

4. Statistics Slides Class 10: Retrieved July 31, 2014, from http://www.csun.edu/~an73773/SlidesClass10F09.pdf