Question
- Assignment 1: Bottling Company Case Study
Imagine you are a manager at a major bottling company. Customers have begun to complain that the bottles of the brand of soda produced in your company contain less than the advertised sixteen (16) ounces of product. Your boss wants to solve the problem at hand and has asked you to investigate. You have your employees pull thirty (30) bottles off the line at random from all the shifts at the bottling plant. You ask your employees to measure the amount of soda there is in each bottle. Note: Use the data set provided by your instructor to complete this assignment.
Bottle Number |
Ounces |
Bottle Number |
Ounces |
Bottle Number |
Ounces |
1 |
14.23 |
11 |
15.77 |
21 |
16.23 |
2 |
14.32 |
12 |
15.80 |
22 |
16.25 |
3 |
14.98 |
13 |
15.82 |
23 |
16.31 |
4 |
15.00 |
14 |
15.87 |
24 |
16.32 |
5 |
15.11 |
15 |
15.98 |
25 |
16.34 |
6 |
15.21 |
16 |
16.00 |
26 |
16.46 |
7 |
15.42 |
17 |
16.02 |
27 |
16.47 |
8 |
15.47 |
18 |
16.05 |
28 |
16.51 |
9 |
15.65 |
19 |
16.21 |
29 |
16.91 |
10 |
15.74 |
20 |
16.21 |
30 |
16.96 |
Write a two to three (2-3) page report in which you:
- Calculate the mean, median, and standard deviation for ounces in the bottles.
- Construct a 95% Confidence Interval for the ounces in the bottles.
- Conduct a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Clearly state the logic of your test, the calculations, and the conclusion of your test.
- Provide the following discussion based on the conclusion of your test:
- If you conclude that there are less than sixteen (16) ounces in a bottle of soda, speculate on three (3) possible causes. Next, suggest the strategies to avoid the deficit in the future.
Or
- If you conclude that the claim of less soda per bottle is not supported or justified, provide a detailed explanation to your boss about the situation. Include your speculation on the reason(s) behind the claim, and recommend one (1) strategy geared toward mitigating this issue in the future.
Your assignment must follow these formatting requirements:
- Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides. No citations and references are required, but if you use them, they must follow APA format. Check with your professor for any additional instructions.
- Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.
The specific course learning outcomes associated with this assignment are:
- Calculate measurements of central tendency and dispersal.
- Determine confidence intervals for data.
- Describe the vocabulary and principles of hypothesis testing.
- Discuss application of course content to professional contexts.
- Use technological tools to solve problems in statistics.
- Write clearly and concisely about statistics using proper writing mechanics.
Sample paper
Hypothesis Testing
The mean for the data is 15.854 ounces. The mean is a measure of central tendency, or how values in a distribution are spread. The median is also a measure of central tendency, and estimates the central value. If the data does not have outliers, the mean and median may be close. Outliers significantly affect the mean, but hardly affect the median. From the data, the mean is 15.854 and the median is 15.99. This means that data did not have significant outliers. On average, most bottles had 15.854 ounces of soda, meaning that they fell short of the required 16 ounces of soda. Cumulatively, only a few had 16 or more ounces of soda. The standard deviation indicates how values are spread around the mean. Normal standard deviation ranges between -3 and +3 standard deviations. The standard deviation of 0.661 indicates that the values fall close to the mean.
The following are the hypotheses applied in analyzing the data.
H_{0}. The volume of soda in the bottles is equal to 16 ounces.
H_{1}. The volume of soda in most bottles is less than 16 ounces.
The 95 percent confidence explains where the population mean would fall. From the calculations, there is a 95 percent chance that the population mean will fall between 16.0907 and 15.6172. The significance level/critical region is (1-0.95) = 0.05. From the tables, the z value is 1.65. This means that 1% of the area falls to the right of the z value while 95% of the area falls to the left in the graph. The test value is: = -1.209. The test value falls within the critical region. As such, the null hypothesis is rejected. This means that the volume of soda in the bottles is not equal to 16 ounces. In other words, there is a significant difference in the expected ounces and the volume that is actually put in the bottles.
There are a number of possible causes in this scenario. The first cause could be a type I error. A type I error occurs when the null hypothesis is rejected yet it is true (Bluman, 2008). This could occur due to miscalculations or a wrong judgement. Another possible cause is machine error. Another possibility is the presence of a defective machine that is leading to incidences of excess and/lower ounces of soda per bottle. Another cause could be malicious activities by staff to put less ounces per bottle, leading to extra ounces of soda being available for sale, although illegally.
The company should conduct a thorough analysis of the machines used in filling the soda bottles to ensure the defective machines are replaced. Alternatively, a more accurate calibration of the machine will help in standardizing the amount or volume discharged per machine. There is also need to investigate whether some employees could be intentionally manipulating the process such that extra soda bottles are produced for sale. This will help in shedding light on the source of this anomaly. It will be possible to fix the problem once the cause is identified.
Reference
Bluman, A. G. (2008). Elementary statistics: A brief version : Allan G. Bluman. Dubuque: McGraw-Hill Companies.
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