The investigation to ascertain the complaints launched by the customers as directed by the manager were sought by calculating the mean, median, and the standard deviation from details provided in the case. As such, the results and findings sought in this study are based on the sixteen bottles selected randomly for the case. Results were derived through the use of Statistical Package for Social Sciences (SPSS). The descriptive statistics from the analysis reported the mean ounce and the confidence interval of the study as 15.854 and 95% respectively. Further results from the descriptive statistics reported the median as 14.8. The descriptive analysis can be identified as follows;
In the calculations, the margin of error is calculated by using the formulae . The explanation of the equation indicates that the critical value is given by α = 1 – (confidence level / 100) =
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Therefore, the critical value denoted by Z=
The critical interval is given = = 15.854 =
CI=16.091 or 15.617
From the analysis conducted in this study, we can be 95% confident that the mean ounce of the bottles lies between 16.19 and 15.62 with a margin of error of 0.025. In order to understand the complaints raised by the customers, there is the need to formulate the hypothesis assuming that the mean is lower than 16 ounces as articulated in the case. The formulation of the hypothesis results in the following;
H 0 = the bottles of the brand of soda contained the advertised 16 ounces of the product (
H 0 = the bottles of the brand contained less than then the advertised 16 ounces of the product (
The solution from the hypothesis testing can be identified as follows;
Calculating the test statistic -
15.854-16
15.854
=13.92
The next step is to set the rejection Region.
Rejection region is given by /Z/ > 16.0. Given that the findings demonstrate that 13.92 is less than 16, therefore, we reject the null hypothesis and confirm that the mean ounces is less than 16. This further confirms customers’ assertion that the mean ounces of the bottles is not equal to 16 ounces. Nevertheless, there are three possible causes that can be attributed to the measurements reported. First, the measurements could have resulted from poor or incorrect calibration. Moreover, the incorrect calibrations could have been caused by a mechanical problem that was not realized by the company employees.
In addition to the failure to standardize the system that elicits inconsistencies through the automation process, there are concerns that the whole process could be attributed to causing the errors. These three problems can be accounted for by the failure to carry out a thorough quality control check that could have helped detect the inconsistencies in the weight of the bottles when packaging the product.
The confirmation of customers’ assertions that there are less than sixteen ounces in a bottle through the hypothesis testing provides a platform to embrace strategies that will prevent these problems from being experienced in the future. The strategies that need to be implemented by the company can be identified as follows;
First, there is the need to adopt the statistical quality control purposely for determining the lower and the upper limits. This will ensure that that the management makes a decision that any bottle that’s not 16 ounces is identified. Second, the equipment should be calibrated clearly and the system automated to avoid manual and reading errors. A further recommendation would entail monitoring and inspecting the packaging process to ensure that all requirements are met before the product is released by the company.
