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 a sample of 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.
Use the data provided in attached Excel sheet. Use 4 decimals of accuracy for all statistical calculations.
Write a two to three (2-3) page report in which you:
- Calculate the sample size, 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
a. 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
b. 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 studentâ€™s name, the professorâ€™s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.
- Be sure to read the rubric contained in Week 10 â€“ Week 10 assignment 1. This rubric tells you exactly how I have to grade the paper.
Compute a 95% confidence interval for the data.
Use 4 decimals of accuracy.
2. Which Distribution you are using (Z, t, X2, or F) and why you are using that distribution?
3. Degrees of Freedom (df), if applicable
4. Value of E, if applicable
5. Lower Limit of the confidence interval
6. Upper Limit of the confidence interval
7. Conclusion based on the confidence interval as to whether the bottles are being filled correctly. That is, is 16 oz in the interval?
Example: These are not the correct answers
2. Distribution: t distribution Why: because Population standard deviation is unknown and n >=30
3. df: 29
4. E: 0.2367
5. Lower Limit: 15.4596
6. Upper Limit: 15.9104l
7. Conclusion: Since 16 zo in not in the confidence interval, I concluded that the process is not filling bottles correctly.
Hypothesis Test: The third intermediate assignment is to conduct a hypothesis test with a level of significance of 0.05. Use 4 decimals of accuracy. By Sunday May 29, send me an email with
2. Null Hypothesis
3. Alternative Hypothesis
4. Tail Test?: State whether this is a Left Tail, Right Tail, or Two Tail test.
5. Which Distribution you are using (Z, t, X2, or F) and Why you are using that distribution?
6. Degrees of Freedom (df), if applicable
7. Value of the Test Statistic
8. Approach: State whether you are using the Critical Value(s) or P-value approach
i) If using the critical value(s), state the critical value(s)
ii) If using the p-value approach, state the p-value
9. Reject?: State whether you Reject H0 or Do Not Reject H0 .
10.Conclusion: Based on the hypothesis test as to whether the bottles are being filled correctly.
Example: These are not the correct answers
1. Name: Gerry Jenkins
2. Null Hypothesis: Ho: Î¼ = 16
3. Alternative Hypothesis: Ha: Î¼ â‰ 16
4. Tail Test?: – Two Tail test.
5. Distribution: t distribution Why: because Population standard deviation is unknown and n >=30
6. df: 29
7. Test Statistic: – 1.7689
8. Approach: Critical Value(s)
i) critical value(s): -1.6450, +1.6450
9. Reject H?: I reject Ho
Conclusion: The bottles are not being filled correctly.