Bottling Company - Case Study Example

Bottling Company Case Study John Doe Bottling Company Case Study Several lodged by complaints say that the soda in the bottles is less than sixteen ounces. The scope of this assignment is to conduct an investigation on this claim. In order to conduct the investigation, 30 bottles were randomly picked up from the filling line. The following paragraphs present the result of the investigation. Sample Descriptive StatisticsData set consists of n = 30 values shown in Table 1. According to the statistical concept, each value in the set is considered to continuous data.

Central tendency of the set, in this investigation, is expressed through mean, median, and standard deviation. Table 1. Sample data set ObservationOuncesObservationOuncesObservationOunces114.501115.002114.10214.601215.102214.20314.701315.002314.00414.801414.402414.90514.901515.802514.70615.301614.002614.50714.901716.002714.60815.501816.102814.80914.801915.802914.801015.202014.503014.60Mean of the set, X mean: 14.87 ouncesMedial of the set, X median : 14.80 Standard deviation of the set, STDV: 0.

55The 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. Confidence Interval 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). Hypothesis TestIn 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 (“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%. Ho: The bottle contains 16 or higher ounces of sodaHa: The bottle contains less than 16 ounces of sodaIn symbol, it can be expressedHo: μ = / > 16 ouncesHa: μ < 16 ouncesBased 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 - μ) / SE = (14.87-16.0) / 0.1 = - 11.25.

Based on degree of freedom, df = 29 and significance level 5%, the “t critical” value is 1.699. Based on test statistics – 11.25 and alpha= 0.05 “p” value is obtained; p(t=-11.25) = 0.00001.The above test reveals:1. For left tail test t = - 11.24 < t critical = 1.699; null must be rejected2. P = 0.00001 < alpha = 0.05, the result is significant; null must be rejectedConclusionThis assignment conducted a hypothesis test using thirty random sample values. It shows that the population mean of soda in a bottle is less than sixteen ounces.

The reasons could be (1) measuring device is not working properly, (2) vibration may be causing spilling of soda after the filling of the bottle (3) managers are intentionally pouring less soda to show higher profit. This study recommends the upper management to investigate and control above-mentioned factors and conduct the same investigation after two weeks. ReferenceWhat is Hypothesis Testing. (n.d). Retrieved from http://stattrek.com/hypothesis-test/hypothesis-testing.aspx