Assignment 1: Bottling Company Case Study
Math 300 – Statistics
June 9, 2014
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.
In this case, ...view middle of the document...
The result of the standard deviation lets me know how the numbers in a set are going to be spread out. The Variance formula for calculating the variance is (s2) = Σ [(xi - x̅) 2]/n. The result for our standard deviation is 0.1936227.
A different way of calculating the boundary by a single value when it’s given a range of possible estimates is to determine the confidence coefficient. A confidence interval (CI) is an estimated range of a statistic. These estimates are determined by the confidence coefficient. The bigger the probability that the interval contains the parameter, the better the range. Confidence intervals are used to indicate the dependability of an estimate. The confidence level of a test sensitivity depends on the sample size. Tests completed on lesser sample sizes (e.g. less than 30 samples) have broader confidence intervals, indicating larger imprecision. Using 95% confidence interval for tests sensitivity is an essential measure in the validation of a test for value assurance.
The margin of error known by the standard deviation over the square root of the sample size is 0.1936; and our calculated upper and lower confidence intervals calculated are: 14.6763 and 15.0636
“The usual process of hypothesis testing consists of four steps. Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true.” (Wolfram, 2013). I am asked to conduct a hypothesis test to determine if a bottle contains less than 16 ounces. The hypothesis formula is H0 µ ≥ 16; Ha µ < 16. My Z0 value is -1.960 because I am testing the 2nd hypothesis that is less than 16 ounces. The standard deviation (symbol: α) given in our problem is 0.05. The statistics test, that is the main goal in the hypothesis test, is given by the formula (µ-n)/STD. The result of the test is equal to -2.08842. The null hypothesis’ level of significance is 0.05, at minimum.
At hand, I have sufficient evidence to claim that the company’s product contains less than the advertised 16 ounces. A number of factors might influence or be accountable for reducing ounces in each bottle. To start with, technical failures might totally effect production. In addition, natural disasters, such as floods and...