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# Bottle Case Study

Submitted By lewiskinda
Words 444
Pages 2
The purpose of this paper is to do a case study of a bottling company. The scenario is: 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 of 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. Use the data set below.
Bottle
Number Ounces Bottle
Number Ounces Bottle
Number Ounces
1 14.5 11 15 21 14.1
2 14.6 12 15.1 22 14.2
3 14.7 13 15 23 14
4 14.8 14 14.4 24 14.9
5 14.9 15 15.8 25 14.7
6 15.3 16 14 26 14.5
7 14.9 17 16 27 14.6
8 15.5 18 16.1 28 14.8
9 14.8 19 15.8 29 14.8
10 15.2 20 14.5 30 14.6

Calculate the mean, median, and standard deviation for ounces in the bottles. The mean is found by getting a total of all the ounces in the bottles. The ounces total, 446.10 and divided by the number of bottles of 30 is 14.87. The median is the midpoint of the data array which is when the data is sorted by size, the median is 14.8. The standard deviation is found by taking each value in the chart and subtracting the mean and squaring the value; get a total sum of the value of the squares and divide by the number of values minus one. The standard deviation is .55.
Construct a 95% confidence interval for the ounces in the bottle. The 95% confidence interval can be found by using the t distribution. The sample mean plus and minus (2.045) times the standard deviation/ square root of 30. The confidence interval is 95% in Table F and the df = 29 which is 2.045.
14.87 – 2.045 times .55/square root of 30 = 14.66
14.87 + 2.045 time .55/square root of 30 + 15.07
The 95% confidence interval is between 14.66 and 15.07. This means that there is a 95% chance of ounces in the bottles of soda is between 14.66 ounces and 15.07 which is less than the standard that the soda should be of 16 ounces.

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