INFERENTIAL STATISTICS AND FINDINGS 2
Inferential Statistics and Findings
Following the American Psychological Association Style Guide
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Introduction
During week five’s individual assignment, we created an inferential statistics (hypothesis) test using the research question and two variables ones learning team developed for the week two Business Research Project Part 1 assignment. This will include two aspects (1) the research question and (2) mock data for the independent and dependent variables. Next, we will determine the appropriate statistical tool to test the hypothesis based on the research question then, conduct a hypothesis test with a 95% confidence level, using the statistical tool. Finally, we will interpret the results of our findings.
Creating an Inferential Statistics (Hypothesis) Test
According to Lind, Marchal, Wathen & White (2015), inferential statistics is the process of “sampling from a population with the objective of estimating properties of a population” (Lind, Marchal, Wathen & White, 2015, p. 5). As we created an inferential statistics (hypothesis) test on the research question of: does promotions have a significant effect on sales revenue, we must understand that at times, limited set of data will require a decision, such as being unable to tell if the null hypothesis is true or false and if the alternative hypothesis is true or false.
Background
Reeds Valley Market is a small local town main grocery store with about 150 employees, located in Winesingberg, MO. Reeds Valley commitment is to provide the finest fare-succulent and delectable perishables as well as the most monitored and maintained quality standards available every day. When it comes to produce, Reeds Valley Supermarket ensures that they offer the largest variety of high quality produce both organically and naturally through locally sourced farmers and seasonal picks of produce. However, they are faced with a business problem. Reeds Valley Supermarket is faced with a business of sales dropping because of a new competitor and they would like to introduce a new promotional strategy to attract new customers, but they need to know the influential factors that promotions have on sales revenues. The promotional strategy is implementing a Loyalty Rewards Program. What this is, is that for every $100 spent on groceries using ones Reeds Card, they will receive $20 in free groceries their next purchase. The Reed’s Cards will initially be given out at the cash registers to customers when they purchase their goods and they can accumulate their points for the next six months. With this plan no extra resources are being used on marketing and its current customers and word of mouth will help in getting the word out about the card. The overall expense of the distribution of these cards would be minimal this way, so if it was unsuccessful there would not be as much overhead costs sank into the program. At the very least the most loyal customers got discounts for six months and that might keep them around after or if the card goes away.
Determining the Appropriate Statistical Tool to Test the Hypothesis
The hypothesis statements based on the research question for Reeds Valley Supermarket is (1) there is no significant relationship between promotional strategies and sales revenue, and (2) there is a significant relationship between promotional strategies and sales revenue. The appropriate statistical tool to test the hypothesis is the two-sample T-test. This type of statistical tool is most common for hypothesis testing. The two-sample T-test will “test a hypothesis about the mean population difference between paired or dependent observations” (Lind, Marchal, Wathen & White, 2015, p. 364). For hypothesis testing, Reeds Valley Supermarket is interested in the distribution of the differences in the sales revenue of its Reeds Card Rewards Program. The T-test will allow the Learning Team C to answer the hypothesis by either accepting the null hypothesis or rejecting it. Based on the data calculations, the null hypothesis is false.
Conducting a Hypothesis Test with A 95% Confidence Level
Before we can conduct a hypothesis test, we must write out a hypothesis statement with a 95% confidence level, using the two-sample T-test statistical tool, we must keep in mind that this is the level of significance of the probability of rejecting the null hypothesis when it is true. See
Appendix A attached for figures. A 95% confidence level for the population mean is 21.84 and 47.16 for the promotions. The sales revenue is 374.34 and 992.25. This shows that the data is 95% of the time consistent within those ranges.
An Interpretation of the Results and Providing Findings
After determining the appropriate statistical tool to test the hypothesis, it was important to then state both the null and alternative hypothesis. This aspect allowed one to be able to cover the whole aspect of the hypothesis rather than just part of a range. Calculating the hypothesis was based on the two-tailed test in which, calculated the probability of deviation in either direction from the null hypothesis. Based on the collection and data calculations performed, one is inclined to reject the null hypothesis.
Providing ones’ findings will be supported in Appendix A, the statistical findings should show evidence that the distribution was normal, resulting in the mean of 34.5 and standard deviation of 4.92. The 95% confidence level of $374.4 and $992.3, Learning Team C is confident that Reeds Valley Supermarket’s implementation of new promotional strategies will work. It is important to keep in mind that only one variable can have superiority over the other. A T-test is when population deviation is unknown. The shape of the distribution data depends on the appropriate measure. This shape can be normal, right (positively) or left (negatively) skewed. Looking at the mean and median, they are approximately the same as the distribution. It is critical to understand that the skewness measure the shape. Looking at the attached Appendix A, the skewness is slight right.
Research Question Answers
The answers to the research question the hypothesis statements based on the research question for Reeds Valley Supermarket is (1) there is no significant relationship between promotional strategies and sales revenue, and (2) there is a significant relationship between promotional strategies and sales revenue. As well, the research question also remains will Reed Valley Supermarket’s promotional methods work?
The 95% confidence level of $374.4 and $992.3, Learning Team C is confident that Reeds Valley Supermarket’s implementation of new promotional strategies will work. It is important to keep in mind that only one variable can have superiority over the other. A T-test is when population deviation is unknown.
Summary of the Challenges Resulting from the Research
The challenges resulting from the research involve the 5% deviation level in accordance with the 95% confidence level of $374.4 and $992.3, Learning Team C is confident that Reeds Valley Supermarket’s implementation of new promotional strategies will work. With the 5% variance in not a 100% confidence level for the results of this research, it is possible that the amount of revenue that Reeds Valley Supermarket would obtain could be more or less than the 95% confidence level.
Summary of the Implications Resulting from the Research
The summary of the implications resulting from the research determine that Reeds Valley Supermarket can successfully minimize the expense of costly marketing practices through a promotion card on their goods and services and also adequately fairly compete with their competitors through word-of-mouth promotion of the promotion card, as well as through their loyal customers in the store of Reeds Valley Supermarket.
Potential Research Efforts with an Inclusive Result
Other research efforts that could accompany the Reeds Valley Supermarket’s strategy for increasing its revenue in opposition with its competition would be to conduct a T-test on whether or not low cost marketing strategies would work, or perhaps even low cost marketing strategies that would involve technological intervention such as social media and the Internet.
New Research Questions to Find Definitive Results
Some new research questions that may help to find more definitive results would be: who are the clientele of Reeds Valley Supermarket? Why does this clientele choose Reeds Valley Supermarket over its competitors? What do these clients like most about Reeds Valley Supermarket? What do these clients of Reeds Valley Supermarket like least about the store? What do these clients think can be improved about the Reeds Valley Supermarket? What do they think Reeds Valley Supermarket is doing well? How do the clients of Reeds Valley Supermarket think about the promotion card? Would the clients of Reeds Valley Supermarket spread the word about the promotion card to their friends, family and colleagues? Would the promotion of the card be successful if it the promotion continued beyond the six month testing period? Are there other ways that Reeds Valley Supermarket can successful compete with its competitors? What are some of the things that the competitors of Reeds Valley Supermarket are doing that are working that Reeds Valley Supermarket can adapt on and incorporate in their promotion strategies?
Recommendations Based on the Results
Based on the results of this research Reeds Valley Supermarket should introduce their promotions card for an indefinite period of time in order to secure their customer base. As well, they should do further research into surveying and polling their customers to discover what they like most and what they like least about Reeds Valley Supermarket so that they are making more of an effort in order to meet the needs of the clientele at Reeds Valley Supermarket. Along with these recommendations, Reeds Valley Supermarket also needs to start looking into and investigating the strategies that their competitors are using and seeing how they can adapt these successful strategies in order to win back some of their customer base that they have previously lost to their competitors.
Further research would involve television marketing sales. Here are some of the inferential statistics that are involved with Reeds Valley Supermarket engaging in this research. Inferential statistics: this project aims to determine whether there is a difference in the mean total monthly sales for stores using television advertising and the mean total monthly sales for stores using online advertising. The following table summarizes the data in the accompanying Excel file for the two samples:
Television Online
Mean 101,135.33 99,206.13
Std. Dev. 4,772.7624 4,351.5520
Count 24 48
Since the population variances are not known, and one of the sample sizes is less than 30, the appropriate statistical test to use is a T-test of two independent means. The hypothesis test is as follows:
Hypotheses: Would online television advertising work for Reeds Valley Supermarket in order to increase their revenue and help them to successfully compete with their competitors?
Null: The null quotient variable is that online advertising would not help Reeds Valley Supermarket increase its sales.
Alternative: An alternative to online television advertising could be online advertising that does not involve television, however visuals, photographs, etc., even sound.
Critical value: Assuming that the variances are equal, the number of degrees of freedom is nTelevision + nOnline – 2 = 24 + 48 – 2 = 70. Assuming that the level of significance is 5% (α = 0.05), the critical t values with 70 degrees of freedom are t = - 1.994 and t = 1.994.
Test Statistic: the test static would be in determining if the competitors of Reeds Valley Supermarket are also using online television advertising. The value is 1.717 between the two critical values.
The corresponding p-value is 0.0904.
Decision: Since the test statistic value of 1.717 is between the two critical values, the decision is to fail to reject the null hypothesis. Alternatively, since the p-value of 0.0904 is greater than the level of significance, the decision is to fail to reject the null hypothesis. There is insufficient evidence at the 0.05 level of significance to support a claim that there is a difference in the mean total monthly sales for stores that use television advertising and stores using online advertising.
The conclusion of the hypothesis test is that there is no difference between the mean values of the two samples, which implies that there is no difference in the population values. The null hypothesis is not rejected because the p-value of 0.0904 indicates that there is a 9.04% chance of obtaining the observed difference in the means through random chance alone. Since this probability is greater than the level of significance, there is not sufficient reason to believe that the observed difference is the result of anything other than random chance. Thus, there is not enough evidence that the difference is statistically significant.
Recommendations for this New Variable
Online television advertising would be a good alternative for Reeds Valley Supermarket to venture into in order to increase its revenue base.
Conclusion
It is important to keep in mind that when performing this type of hypothesis testing, the hypothesis will be conflicting; therefore, the null hypothesis will never prove to be true, rather it will state whether one has enough or not enough evidence to reject such a hypothesis. One must also remember that such evidence is not enough to prove that the alternative hypothesis is true. This just happens to be evidence in the alternative hypothesis favor. Based on the results of this research Reeds Valley Supermarket should introduce their promotions card for an indefinite period of time in order to secure their customer base. As well, they should do further research into surveying and polling their customers to discover what they like most and what they like least about Reeds Valley Supermarket so that they are making more of an effort in order to meet the needs of the clientele at Reeds Valley Supermarket. Along with these recommendations, Reeds Valley Supermarket also needs to start looking into and investigating the strategies that their competitors are using and seeing how they can adapt these successful strategies in order to win back some of their customer base that they have previously lost to their competitors.