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3 pages/≈825 words
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APA
Subject:
Mathematics & Economics
Type:
Case Study
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English (U.S.)
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Topic:

The Bottling Company Case Study

Case Study Instructions:

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.
(See Attachment)
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:
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.
Or
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 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.

Case Study Sample Content Preview:

Bottling Company Case Study
Name
Course
Instructor
Date

Frequency Table ValueFrequencyFrequency %1426.6714.113.3314.213.3314.413.3314.5310.0014.6310.0014.726.6714.8413.3314.9310.001526.6715.113.3315.213.3315.313.3315.513.3315.826.671613.3316.113.33
Calculate the mean, median, and standard deviation for ounces in the bottles.
Mean= 446.1 /30=14.87
Median= (14.8+14.8)/2=14.8
Sample Standard deviation= 0.5503
The demand and standard deviation are the two most important measures of central tendency and dispersion that facilitate hypothesis testing. The median is the value at the middle of the frequency table and is typically closer to the mean and mode.
Construct a 95% Confidence Interval for the ounces in the bottles.
Standard error= the standard deviation/ Square root of the sample
The 95% measure confidence range, 1.960σ = Mean (1.96) ± (standard error)
Standard error= s.d/√30= 0.5503/5.4772=0.1004
At 95% confidence interval then is 14.87 ±1.96 (.1004) =14.67≤ x ≤15.07
Hence the value lies between 14.67 and 15.07
Hypothesis testing for the claim aim that a bottle contains less than sixteen (16) ounces is supported
In conducting the hypothesis test there is a need to state the claim being tested, based on the assumption that it is false. After stating the hypothesis then expressing the statement in mathematical signs is the next step and this depends on the claim being tested where one can use the equal sign or inequalities. The statement with the inequality is the alternative hypothesis while the original statement is the null hypothesis. After this then analysis of the sample data provides information to facilitate the decision making on whether to reject or accept the null hypothesis. As such, both the standard deviation as the test score test statistics and in this case the z test was used. The significance level and the distribution are identified. After this then interpreting the results is dependent on comparing the test score calculated and the critical values.
Calculations
H0: µ=16
H1: µ Ë‚ 16
For the z statistics Z 0.05= -1.645
Z score=x̄-x/ s.d√30= 14.87-16/ (0.5503/√30)=-1.13/0.1004= -11.2471
Given that-11.2471 is lower than -1.645, then we do not accept/ we reject ...
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