Inferential Statistics and Findings: Generating a Hypothesis
The aim of the paper is to generate a hypothesis with the use of research questions and two variables- dependent variable: sales/revenue and independent variable: interest rates. In addition, the paper uses a statistical technique for testing the hypothesis at 95% confidence interval while interpreting the results. XYZ Corporation is a US-based company that majors in home improvement and construction.
Moreover, the company operates in various big-box format stores across the United States. Nevertheless, XYZ Corporation wants to determine the effects of interest rates and sales on its future profitability, therefore, the company approached a research team that suggested the below research question.
Is there a relationship between federal (Feds) directed interest rate (ID) and sales /revenue (DV) on future profit of XYZ Corporation?
H0 = XYZ Corporation’s future profits are not determined by interest rates and sales/revenue
H1 = XYZ Corporation’s future profits are determined by interest rates and sales/revenue
Hypothesis tests with a 95% confidence level
The veracity of the null hypothesis depends on data as well as the objective of significance tests to estimate the likelihood, hence the P-value, which underscores that the occurrence is an issue of chance. In this case, if the Pearson Correlation is less than 5% it means that the null hypothesis is rejected.
However, if the P-value is greater than 5% then it means the statistical test fails to reject the null hypothesis (Gupta, 2012). Data was indiscriminately selected from 382 observations with respect to interest rates and sales of XYZ Corporation.
Interpretation of the results and findings
Statistical analysis demonstrates that this is a normal distribution, with a mean of 10.97644 and standard deviation of 10.14628 for sales (Table 1). In this case, sales were observed between $0.00 and $89.00. Changes in the federal interest rates could help determine sales of XYZ Corporation.
In addition, the mean and standard deviation for interest rates were observed at 9.695538 and 7.836266 respectively (Table 2). High-interest rates are highly likely to inhibit any profit making from lack of sales. While low-interest rates by the federal government may lead to increased sales.
Again, it demonstrated a 95% confidence interval (sales:1.020716, interest rates: 0.789369) this implies that XYZ Corporation can be about 95 percent confident that sales and interest rates will lead to an increased future a profit. Because the confidence interval of sales corresponds to the value of alpha, which is 1 indicates that there is no significant correlation between sales and future profit of XYZ Corporation.
However, the results are empirically reliable. When it comes to interest rates the confidence interval is less than 1, statistically the test fails to refute the null hypothesis, an aspect that demonstrates statistical significance of the test (Monette, Sullivan & DeJong, 2011).
Table 1. Descriptive statistics showing XYZ Corporation Sales
|Confidence Level (95.0%)||1.020716|
Table 2. Descriptive statistics showing XYZ Corporation Interest Rates
|Confidence Level (95.0%)||0.789369|
Gupta, S. K. (2012). The relevance of confidence interval and P-value in inferential. Indian Journal of Pharmacology. Retrieved on June 9, 2016, from statistics http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3271529/
Monette, D. R., Sullivan, T. J., & DeJong, C. R. (2011). Applied Social Research: A Tool for the Human Services (8th ed.). Belmont, CA: Brooks/Cole.
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