Question

MAT 300 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
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Answer 1

1. Calculate Mean Median and Mode.. ( from observation)
Mean = Total sum/ Total observations = (x bar)
Median = Mid value
Mode = Maximum occurring value

2. Construct a 95% Confidence Interval for the ounces in the bottles
Variance = summation of [ (x-x bar)^2/n) ]
standard deviation = sq rt (variance)
standard error = standard deviation/ sq rt (n)
Marginal Error = Critical value * standard error
Confidence interval = Mean +/- Margin of error
... where, n is sample population, critical value = 1.96 ( 95% confidence level)

3. Conduct a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported

We will go for Z test as the sample size n >or= 30
Null Hypothesis H0: u =16
so, alternate hypothesis H1: u < 16
z = [ (x bar - u)/ ( standar deviation/ sq rt (n) ]

where u = Mu = 16

Answer 2

refer the graph to accept the null hypothesis, if the value is greater the 1.96 or smaller the -1.96 then we reject the null hypothesis and select the alternate hypothesis.. i.e soda is less the 16 ounce..


Next step find the root cause, which can be anything and prepare a strategy to control the variation.