The Bulk Mail Entry Unit
Introduction
The Bulk Mail Entry Unit is an essential part of the postal service as it is the area where mailers take their bulk mails for acceptance for postal services. This unit ensures that the mails are charged as they should and that
Step 1: Hypotheses Formulation
Given the information the following hypotheses of correlation are formulated to help in the analysis and decision making. However, it is important to assign representative letters to the variables to make the analysis mathematical and easier to follow. So, let μ 1 represent the mean earnings before the auditing of the postal service charges. Let μ 2 represent the mean of the additional revenues after audit has been done, and μ 3 represent the mean earnings if services had been charged according to the recommendation of the audit report. Therefore, it is a fact that if the audit report were to be followed then μ 1 + μ 2 = μ 3 or μ 3 – μ 2 = μ 1
HO: μ3- μ 1 = $1,000,000
H1: μ 3- μ 1 > $1,000,000
That is to say that if the null hypothesis is correct, the difference between the mean for expected revenues (3) and collected or observed revenues (1) should be $1,000,000. Otherwise, if it is greater than that our null hypothesis fails and calls for restating. These hypotheses will be tested at a significant level of 5%. Both SPSS and Microsoft Excel are used for the analysis. Excel is used to compute the R1 + R2 = R3 where Rs stand for revenues realized, additional revenues and expected revenues respectively. The SPSSS is then used to compute t-test statistics.
Step2: Assumptions
It is assumed that the revenues are normally distributed about the mean revenues generated by the BMEUs (Hinton 234). This implies that since the sample is randomly drawn from a normally distributed population, the samples belong to a sampling distribution that exhibit normal distribution about the mean. Consequently, the implication is a sample that is expected to exhibit a mean identical of the source population (Wong et al 613). While a population bearing the property of a standard normal distribution will have a distribution N (0, 1), we assume that the source population for the sample has a distribution N (1,000,000; 2,857,594.90). Therefore, it is essentially important to assume that the additional revenues (difference between expected revenues and collected revenues) are normally distributed about the mean of $1 000 0000.
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Step3: Test Statistic
Paired sample t-test is used to assess the hypotheses. First, the each collected revenues is added to the corresponding additional revenue such that we have a third variable for the revenues that would be collected if the BMEU charged prices in line with audit recommendations and expectations. The test is one-tailed and directional because we are interested in knowing whether the mean difference is greater than or equal to $1 000 000.
Step 4: Test Results, Implication and point estimation
The results of the tests are summarised in the appendix 1. The resultant p-value is 0.000 with t = 16.613. Therefore, given that the results fall within the rejection region and the fact that the p-value is significant, and provides sufficient evidence to warrant rejection of null hypothesis. We therefore reject the null hypothesis and conclude that the additional revenue is greater than $1 000 000.
For the point estimator of the additional revenues, we can estimate the mean average additional revenues by the following formula. Let the mean additional revenue be represented by μ and the observed mean above (that is, 1000 000) be x. Then:
μ = x ± tα *(s/√n)
But we know that our hypothesis was rejected hence we only need to add.
μ = 1000 000 + tα *(s/√n)
= 1 000 000 + tα ((2,857,594.90/√ (2693))
= 1 000 000 + (-16.813* 55,065.8675)
= $74 177. 57
Based on the working, we can conclude that the BMEU can make an extra mean revenue of $74 177. 57 if it charges prices based on the recommendations of the audit report.
Works cited:
Hinton P. “Business Statistics Explained” Routledge 2004: 200 – 266.
Wong W. K., Tang, H. Y. & Leung V. C. M. QoS Support and Service Differentiation in Wireless Networks: International Journal of Communication Systems Volume 17 (6): 2004: 591 – 614.
Appendix 1: attachments
