Bottling Company Case Study Example | Topics and Well Written Essays - 500 words

Bottling Company - Case Study Example The above parameters are calculated using Excel built in functions. The mean and median are very close to each other; it shows that the data do not have skews. Standard deviation of sampling data are small, which states that values are close to the mean. In statistics, the population mean is measured through the sample mean. Statistics uses a concept called confidence interval in order to calculate a population mean. This assignment uses a 95% confidence interval to evaluate a range of the population mean. The confidence interval, in this case, is measured using method of unknown mean and unknown standard deviation of the population. The range is achieved using the central tendency values and the critical value of t, and SE. The critical value is calculated using Excel formula T.INV.2T(0.05,29); where 0.05 is the significance level of 95% confidence interval, 29 is the degree of freedom, df = n-1. The t critical = 2.045. The term SE is called standard error; it is calculated using formula STDV / sqrt (n). In this case, SE = 0.1. The upper limit of the interval = X mean + t*SE = 14.87+2.045*0.1=15.08. The lower limit of the interval is X mean +t.*SE = 14.87-2.045*0.1 = 14.66. Thus, the 95% confidence interval is (14.66, 15.08). In this case, customer’s complaint is that the soda in the bottle is less than 16 ounces; however, the company claims that the soda in the bottle is 16 ounces. These two statements give the basis for the hypothesis test (â€Å"What is hypothesis testing†, n.d.). The alternate hypothesis is the population mean is less than 16 ounces; null is the population mean is equal or greater than 16 ounces. The significance level of the test is 5%. Based on the alternative statement, it is advised to conduct a left tail test of mean; for this purpose test statistics is defined as t = (x mean - ÃŽ ¼) / SE = (14.87-16.0) / 0.1 = - 11.25. Based on degree of freedom, df = 29 and significance level