Essay Writing Help on Bottling Company Case Study

The Bottling Company Case Study

Due to the complains raised by customers concerning the amount of ounces contained in a bottle of soda, the following analysis has been done to investigate whether it is true that a bottle of soda contains less than 16 ounces as claimed by most customers. The probable reasons that could have caused this defect are also discussed together with strategies to improve the current situation.

Bottle NumberOunces (x)(x-mean) squared
114.50.1369
214.60.0729
314.70.0289
414.80.0049
514.90.0009
615.30.1849
714.90.0009
815.50.3969
914.80.0049
1015.20.1089
11150.0169
1215.10.0529
13150.0169
1414.40.2209
1515.80.8649
16140.7569
17161.2769
1816.11.5129
1915.80.8649
2014.50.1369
2114.10.5929
2214.20.4489
23140.7569
2414.90.0009
2514.70.0289
2614.50.1369
2714.60.0729
2814.80.0049
2914.80.0049
3014.60.0729
N= 30Summation =446.1Summation=8.7781

Question 1

Let ounces be x and the sample size be n therefore: Mean =summation of x/n

                                                                                                           =446.1/30 = 14.87

Median is the number that appears in the middle when the set of data is arranged in ascending or descending order.

14, 14, 14.1, 14.2, 14.4, 14.5, 14.5, 14.5, 14.6, 14.6, 14.6, 14.7, 14.7, 14.8, 14.8, 14.9, 14.9, 14.9, 15, 15, 15.1, 15.2, 15.3, 15.5, 15.8, 15.8, 16, 16.1

Median=[14.8+14.8]/2 = 14.8

Standard deviation is the square root of variance and variance =summation of [x-mean] squared/n

Therefore standard deviation = square root of [8.7781/30] = 0.5409.

Question 2

If the confidence level is 95% then the significance level is 0.05.To construct a confidence level, the margin error should be calculated, and to get margin error, the critical value should be calculated using the t-distribution table.

The degree of freedom = n-k, k being the number of variables, hence degree of freedom =29.Using the significance level we compute the cumulative probability which is= 1-[0.05/2]=0.975 obtaining a critical value of 2.045 using the t-distribution table.

Therefore margin error = critical value *standard error [standard deviation/sample size]

                                         =2.045*[0.5409/30] = 0.0369

Therefore the confidence interval = 14.87 +/- 0.0369

Question 3: Hypothesis testing

Hypothesis testing is used to test whether calculations results can be trusted. As in this case, the calculations are about ounces contained in a bottle. The test will be used to test whether it is true that the ounces in a bottle are less than the company claims it contain. Hypothesis testing can be grouped into two types; null hypothesis and alternative hypothesis. Null hypothesis, which is denoted by Ho, is the hypothesis of interest. Alternative hypothesis on the other hand is the hypothesis that is tested against the null hypothesis. Alternative hypothesis is denoted by HA.

Calculation

The null and alternative hypothesis is first stated, which is:Ho=16 and HA <16. Using the confidence interval approach, the decision rule for the hypothesis testing states that if the estimator, which in this case is 16 ounces falls within the confidence interval, then we do not reject the null hypothesis but if the estimator falls outside the confidence level, then we reject the null hypothesis

From previous calculation, the confidence interval is 14.87 +/- 0.0369 meaning the acceptance area is between the ranges of 14.83 to 14.91.Since our estimator, which is 16 ounces do not fall within the confidence interval, and then we reject the null hypothesis.

Conclusion

Based on the hypothesis testing performed above, it is therefore in order to conclude that the ounces contained in a bottle of soda is less than 16 ounces. This is because we have rejected the null hypothesis meaning that ounces contained in a bottle of soda is not equal to 16 ounces and that the customers are right.

A number of reasons can cause this defect. The main ones being failure of equipment, lack of inspection of bottles before distributing them, and marketing failure. Equipment failure can interfere with the measurement, especially if the equipment that has failed is one that is used for measuring the ounces contained in a bottle of soda. In addition, marketing failure causes defects when the labels on the bottle are misleading. That is the label written on the bottle is not what is really obtained inside. The defect in the soda bottle content could also be as a result of senior management not inspecting the bottles before they are distributed in order to ensure that the content in the bottle are correct and agrees with the labels on the bottle.

Elimination of these defects will require very good strategies that are long term. The most convenient strategy that this report recommends is quality management practices. This will ensure that the management system is continuously improved. This strategy is characterized by putting in place quality standards and management control that are to be followed in identifying and controlling unforeseen errors to avoid failures of the systems.

References

Ashley, R. (2012). Fundamentals of applied econometrics. Hoboken, NJ: Wiley.