Bottling Company Case Study

Introduction

The customers have been complaining that the ounces in the bottle are less than 16. There are reasons that could be leading to this and the manager has decided to investigate the reason for this. From the case study, the results will be able to tell if the complains by the customers is true. This is achieved by taking at random 30 bottles of soda and recording their ounces and presented for analysis.

Descri ptive statistics

From the data that is sampled from 30 bottles, the mean value of the sample is 14.87 while the standard deviation is 0.55. The mean and the mode are 14.8 and 14.8 respectively. This information is obtained from the descri ptive statistics of the data shown below.

Ounces

Mean

14.87

Standard Error

0.100475879

Median

14.8

Mode

14.8

Standard Deviation

0.550329055

Sample Variance

0.302862069

Kurtosis

0.105226406

Skewness

0.641561718

Range

2.1

Minimum

14

Maximum

16.1

Sum

446.1

Count

30

95% Confidence interval

To conduct the 95% confident interval, we have to follow the z-distribution since the sample size (n) is equal to 30. This means . The confidence interval is therefore calculated using the formula below (Smithson, 2010).

In this case study, n=30, is the sample mean and .

These values are substituted in the formula above to give

(14.87+0.197), (14.87-0.197)

=(15.07, 14.67)

Hypothesis testing

Since the customers have been complaining, we need to test if the mean is lower than 16 ounces. This is done by first formulating the hypothesis that will help us test the study (Wilcox, 2012). The null hypothesis will be the mean ounce is equal to 16 which will be tested against the alternative hypothesis stated as the mean ounce is less than 16. This is mathematically written as

We are going to calculate the z statistic since the value of n=30. This is done using the formula

This is substituted as

Z

Z=-11.25

In this case study, n=30, is the sample mean and

The critical value at

When we compare the calculated value of z and the Z value from the table, it is clear that z-calculated is lower than the z-statistic from the tables. (-).

Therefore, we reject the null hypothesis and conclude that there is enough evidence to make a conclusion based on the study that the mean ounce in the bottles is less than 16.

Reasons for the problem

Since I have concluded that there are less than 16 ounces in the bottles, there are reasons as to why this could happen in the company.

The first reason that can cause the ounce to be less than the expected in the bottles is failure of the machine. The machine could be having less time that it takes to feel the bottle. The machine should be checked to find out if this is the reason for the less than 16 ounces.

Another reason as to why this could be happening is the bottle top size. The bottle mouths could be small such that when the bottle is getting filled, some soda is pouring out. The company should investigate on the changes in the bottle size.

Finally, the belt that the bottles move as they get filled could be moving fast and little time is being taken to fill the bottle. The company should check the speed of the bottle belt and make changes if so that the ounces can be maintained at 16 ounces.