The case study that is being investigated is for a bottling company producing less soda than what is advertised. Customers have complained that the sodas in the bottles contain less than the advertised sixteen ounces. The employees at the company have measured the amount of soda contained in each bottle. There are thirty bottles that have been pulled from the shelves. The manager of the company would like to have a detailed report on the possible causes, if any, for the shortage in the amount of soda or if the claim is not supported explain how to mitigate the issue in the future.

In order to statistically find a cause in the shortage a hypothesis testing is conducted by finding the mean, median, and standard deviation for ounces in the bottles. Constructing a 95 percent interval will establish the mean of the population since the mean of the population is not known. There are thirty soda bottles being pulled for investigation. The mean will be calculated by averaging the amount of ounces in each bottle and dividing the total by the number of bottles.

The data below shows the ounces in each of the thirty bottles that were pulled. The mean among the sample bottles is 14. 87. The calculation to find the mean is to add all the ounces per bottle. The total is 446. 1 divided by the random sample of 30. The average ounces in the bottles are less than 16 ounces. The median for the soda bottles is 14. 8. The median is imputed by dividing the random number of 30 by 2 which equals 15. Arrange the ounces from smallest to largest, and select the number that falls on 15.

This will provide the median for the thirty bottles. The standard deviation for the ounces in the bottles is 0. 55. The standard deviation must be known in order to compute the confidence interval. To find the standard deviation, calculate the individual ounces minus the mean of the ounces and square the total (X-M)2. After the total is calculated, divide by the random count 30 minus 1 (n-1). In order to compute the confidence interval of 95 percent; the mean, standard deviation, and identifying the value must calculated.

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data (Easton & McColl, n. d. ). The confidence interval of 95 percent can be found using a normal distribution calculator. The Z distribution is used in this case study because there are thirty bottles. The Z value is greater than or equal to thirty within the sample size. The Z value of 95 percent is 1. 96. This represents the area on the normal distribution chart between the cutoff points.

The cutoff points on the chart are between -1. 96 and 1. 96. The lower and upper limit will be given to locate the interval using the standard normal confidence interval. Calculate to find the interval by imputing Z. 025 equals 1. 96 stores the answer, in this case, using the Aleks calculator. Enter the mean 14. 87 +/- 1. 96 times 0. 55 divided by square root of 30. The lower limit is 14. 67 and the upper limit is 15. 07. This interval proves the soda in the bottles did not contain sixteen ounces.

In Easton and McColl (n. d) article summarized setting up and testing hypothesis is an essential part of statistical inference. In order to formulate such a test, usually some theory has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved. To verify the claim that the bottles contain less than sixteen ounces of soda a hypothesis test will be performed. To find the null hypothesis that represents the claim to be true or to be used as a basis of argument until it is proven. The null hypothesis is H0 greater than or equal to sixteen ounces.

The alternative hypothesis is H1 less than sixteen ounces. The type of test used is one tailed testing. If using a significance level of . 05, a one-tailed test allots the entire alpha to testing the statistical significance in the one direction of interest. This means that . 05 is in one tail of the distribution test statistic. When using a one-tailed test, it is testing for the possibility of the relationship in one direction and completely disregarding the possibility of a relationship in the other direction (“UCLA: Statistical Consulting Group,” 2007).

The value of the test is calculated by the mean 1 minus mean 2. Therefore, 14. 87 – 16 equals -1. 13 divided by standard deviation 0. 55 divided by square root of random sample 30 equals . 375. The P value is calculated by using the formula P (Z < equal to . 375). The P value is 0. 646. The P value is greater than the significance level of test which is . 05. The answer is the mean of 0. 5 < 0. 646. The conclusion of the test for the null hypothesis is not rejected. This suggests the alternative hypothesis must be true that the soda in the bottles is less than sixteen ounces.

The type of error used in the hypothesis is type I error. There are several causes determining the reason for fewer ounces in the bottles. The air in the lines could prevent the soda from filling bottles, machine may need to be reset to fill 16 ounces to the exact measure, or machine may not be calibrated properly. Issuing a daily calibration of the machinery is a way to avoid the deficit in the future. Statistically the issue could stem from the unknown population of how many customers complained. There could possibly be a million sodas produced with only ten customer complaints.

Therefore, pulling more bottles from the shelves and testing the ounces could show a different alternative hypothesis and may prevent a deficit in the future. Other speculations that determine sodas from not being filled to the top are to keep the soda from overfilling so it is not filled to the top line. It has to have a bit of air in the bottle so there can be room for the liquid. Less soda is in the bottles to expand if it gets heated otherwise the bottle could break. In conclusion, the customers are correct there is less than 16 ounces of soda in the bottle.

Don't use plagiarized sources. Get Your Custom Essay on

Statistic Case Study for Bottle Company

Just from $13/Page

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.