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Assignment 1: Bottling Company Case Study
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. 1. My first task is to calculate the mean, median, and standard deviation for the given ounces in the bottles. In order to complete this task, I transferred the data into an Excel workbook. I proceeded to the statistical functions to calculate the mean, median, and standard deviation. The results are defined in the following Excel image.

2. My next task is to construct a 95% confidence interval for the ounces in the bottles.

The population mean (µ) is the parameter that I will be using for this equation. From the random sample, the value of µ is x=14.92
The confidence level of the based on this sample will be constructed to capture the µ with 95% confidence.
The sample size is n=30 and the population standard deviation is 0.55. According to the central limit theorem, because the sample size is equal to 30, the sample mean x approximately follows a normal distribution with a mean µ and a known standard deviation σ.

Using the following equation, I can substitute in the given information to find the values for the 95% confidence interval. x±1.96(σn )
When I substitute the given information for the values, I get the interval

14.92-1.96(0.5530) ≤ µ ≤ 14.92+1.96(0.5530).

I can be 95% confident that µ lies between 14.72 and 15.12. The Upper Confidence Interval Level is 15.12 and the Lower Confidence

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