One-Sample Hypothesis Testing Cases

The following work will provide statistical analysis on the SpeedX Payment Times case study. The study will apply a one-sample hypothesis test in determining if it is possible to convince the chief financial officer (CFO) about concluding the plan of putting together the stamped self-addressed envelopes and invoices which will be profitable. The decisions will be based on whether the null or alternative hypothesis will be accepted or rejected.   

SpeedX 

SpeedX is a big courier company that is looking for a reduction in customer payment time. The payment usually takes thirty days from the time the clients make a request. The current procedure requires the customers to take back their payment using envelops, which have listed addresses. The amount of time that is used for paying the bills has a mean of twenty-four days and a standard deviation of six days ( University of Phoenix, 2017) . According to the CFO, the time of payment can be minimized by ensuring that the envelope with the stamped personal address and the invoice are provided together to the clients. A calculation of the cash flow, which has been improved from decreasing the payment period by two days, shows that it would be able to pay for the envelops and stamps costs.    

The business analyst in the company is responsible for analyzing data and guiding the senior management in making an informed decision since the student will be acting as the analyst, it will be an opportunity of exercising the statistical skills that have been learned throughout the course. The background information on inferential statistics will also be applied in the case study in making the final decisions ( Adams & Lawrence, 2018) . The inferential statistics, in this case, will start with sampling. The business analyst, in this case, the student, selected 220 customers randomly to take part in the hypothesis postulated by the CFO on delivering the invoice with the personal stamped address envelops.  When the proposal was presented to the CFO, she accepted it and allowed for a pilot study to be carried out. In the recording, the number of days taken before receiving the payment is made (Kellner & Celisse, 2019). The sample group allowed for their invoices to be delivered with the provided personal address. A one-sample hypothesis test is carried out by the business analyst to establish if it is possible to convince the CFO on passing the plan as profitable. The significance level of the test is 0.10, with the analysis being carried out as follows: 

The hypotheses for SpeedX Company are:

Null hypothesis is less or equal to 24

Alternative hypothesis is larger or equal to 24.

The rejection region is to avoid the null hypothesis if t > 1.29.

Test statistics is -6.019 while the p-value is recorded as 3.65.

Decision: since -6.019 is less than > 1.29, then the recommendation would be for the CFO to accept the null hypothesis as the results indicates that the plan is profitable.

Conclusion 

The statistical analysis guided the students in making the final decision. The single sample hypothesis enabled the analyst to advise the CFO on passing the plan of sending the clients their invoices with envelops that have personal address. The process would reduce the delivery time and increase profitability. Conducting the case study enabled the students to follow the steps of the hypothesis testing process, which are: stating the null and alternative hypotheses, setting the alpha, collecting data, calculating the test statistics, constructing the rejection regions, and making the final decision.

References 

Adams, K. A., & Lawrence, E. K. (2018).  Research methods, statistics, and applications . Sage Publications. 

Kellner, J., & Celisse, A. (2019). A one-sample test for normality with kernel methods.  Bernoulli ,  25 (3), 1816-1837. 

University of Phoenix. (2017). Case study - election results and speedx. Retrieved from University of Phoenix, QNT561 website.