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1. To calculate the mean, which is the total sum divided by the total count, we need to add all the number of ounces together and divide this by the total number of bottles. Here the number of bottles provided is 30. So for the mean we get a value of 446.1/30, the answer of which is 14.9. The means of finding the median are by figuring out the middle number, which is usually done by placing all the numbers in a value order and finding the middle number in them. Since we have an even number provided here, we will find the average of the two numbers in the middle that helps to give a more accurate value. So here it will be 14.8/2 +14.8 whose answer is 14.8.
2.
For this, a few statistical references are required. Firstly, we use the mean sample, which was 14.9. as we have selected a 95% confidence interval, the rooms for error in our calculations needs to be calculated.
This is done with the help of the T-score model, the critical value recorded is 1.96. If this value is multiplied with the confidence interval 0.95, the sum of the room of error is calculated 1.86. Hence, the confidence interval of 96% is present somewhere around the mean population interval of 13.04 and 16.76.
3. The next step is to conduct a hypothesis that supports the claim that the bottles contain less than 16 ounces. To begin with this, firstly the hypothesis should be considered as void, that our values are concluded at random or that we have used a different hypothesis, that shows our observations by run by a non-random cause. (StatTrek, 2013).
In this case the null hypothesis says there are 16 ounces in a bottle. To understand the result of this hypothesis, we infer the data set and our values deducted in the previous question in order to get them.
Looking at the data from above, we have a mean of 14.9 and a deviation achieved of 0.55. if we add one standard deviation to the mean, it does not add up to 16 ounces but to 15.45 ounces. This proves that the null hypothesis was incorrect and has been rectified, which shows that the alternate hypothesis will be the correct assessment of the calculation.
4. As it has been proven that there are less than 16 ounces in more than half of the samples, it is needed in time to think over the causes of the less amount since there is no clear data to answer why.
The first cause can be faulty equipment used in the making and filling. It could be possible that the dispensing machine is at fault at reading 16 ounces although the amount is actually less.
This can be the easiest to figure out since the machinery and apparatus can be tested and checked and moreover repaired with the least amount of coat and time.
In order to prevent such errors in the future, maintenance and check on the machine on a regular basis to ensure that no such errors occur in the long run and provide any disappointment to the client.
The second possible cause can be human error; in the form of perhaps incorrect programming to the machinery, negligence and failure on their part to check the faulty equipment or improper techniques applied for bottling.
The steps that can be taken to ensure no faults in the long run can be long and detailed sessions for training and guiding including a Training Needs Analysis to estimate if the employees working the machines and bottling have the proper KSAs required for the job in hand. Otherwise, they can be corrected and trained appropriately. This can be done by providing improved and lengthy careful training for all employees at work that usually helps to eliminate errors to a great extent.
The third and final way to ensure zero mistakes is by the testing method which is used to determine the amount of 16 ounces in the bottles. This test can be carried out multiple times, as a control and experimented form, to figure out where the error lies, and whether it were just a sampling error that can be corrected in the initial stages.
The simplest way to correct this is by maintaining efficient records of all the amounts that have been recorded and catch the problem wherever it occurs first. For this, experts need to come into direct contact with and make different inference and check the tests for validation.
References
Larson, R., & Farber, B. (2009). Elementary statistics: Picturing the world. (Custom ed.). Upper Saddle River, NJ: Prentice Hall.
Green, L. (2013). Mean, mode, median, and standard deviation. Retrieved on December 14, 2013 from http://www.ltcconline.net/greenl/courses/201/descstat/mean.htm.
StatTrek.com. (2013). What is a confidence interval?. Retrieved on December 14, 2013 from http://stattrek.com/estimation/confidence-interval.aspx
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