In this project we were given the case of customer complaints that the bottles of the brand of soda produced in our company contained less than the advertised sixteen ounces of product. Our boss wants us to solve the problem at hand and has asked me to investigate.
I have asked my employees to pull Thirty (30) bottles off the line at random from all the shifts at the bottling plant. The first step in solving this problem is to calculate the mean (x bar), the median (mu), and the standard deviation (s) of the sample. All of those calculations were easily computed in excel.The mean was computed by entering: =average, the median by: =median, and the std.
dev. by: = = std dev. The corresponding values are x bar = 14. 87, mu = 14. 8, and s = 0. 550329055.
The next step in solving the problem is to construct a 95% confidence interval for the average amount of the company’s 16-ounce bottles. The confidence interval was constructed by drawing a normal distribution with c = 95%, a = 0. 050, and Zc = 0. 025. The Zc value was entered into the Z• (z box) function in the Aleks calculator that resulted in a Z score of +1.
96 and -1. 96.We calculate the standard error (SE) by dividing the s by the Square root of n which is the sample size. The margin of error is calculated by multiplying the z score = 1. 96 by the std.
dev. = 0. 5503/the square root of n = 5. 4772. The result is a 0. 020 margin of error.
The margin of error is added to and subtracted from the mean to give two numbers the lower and upper values. The lower value is 14. 85 and the upper value is 14. 89. So, we can say that with 95% confidence the mean of the sample is between 14. 85 and 14.
89.The next step in solving the equation is to complete a hypothesis test. For this test the null and alternative hypotheses must be identified. Since the claim is that the sample is less than the mean the claim of or = to 16oz. So, Ho = >=16oz. We calculate the p value by multiplying x bar by Mo / s / the square root of n.
(14. 87*16/0. 550329055/5. 4772 = 0. 1005) So, we have p = 0. 1005.
Then we ask if p is greater than a (alpha). Since p is greater than a = 0. 10 we decide that there is significant evidence supporting the claim to not reject the Ho. So, we accept the null hypothesis that on average there is less than the advertised 16oz in each bottle.Some of the possible causes of the possible causes of the difference of the average amount of soda per bottle could be that there is a maintenance issue with the machines that dispense the soda into the bottles.
Calibration of the machinery could resolve the issue. A second reason that the bottles contain less than 16oz on average is that there could be an issue with the loss of product between the bottles being filled and the bottle caps being put on.In this case, the bottles would need to be monitored between being filled and being capped to observe any variance in that phase of the bottling process. A third reason that the bottles contain less than 16oz on average could be a faulty measurement process.
If in the filling process the soda is freshly mixed and contains various amounts of air and once the product settles the air is dispersed the bottle volume may be less than it was when it was filled.So if the volume is measured any time before the air is dispersed and the product settles then there would be a random variance in the volume. This can be resolved in many ways, but I speculate that the easiest and most efficient way is to determine the average difference in volume and increase the per bottle volume by that amount. To test the results of each possible solution we must repeat the test of samples after we make adjustments to determine if we achieve success which would be when there is significant evidence to reject the claim.
