Bottle Company Case Study
Bottle Company Case Study
Ron Hobson
Statistics
Professor Derrick Barbee
December 14, 2014
Bottle Company Case Study
Recently customers have complained that our soda bottles have not contained the 16 ounces of soda, which we advertise. To figure out the problem bottles were pulled randomly off of 30 machines. Our calculations concluded that there was a total of 446.1 ounces of soda measured from 30 bottles with an average (Mean) of 14.87 ounces of soda per bottle, with a mode of 14.8. The calculated standard deviation is 0.550329 Now we have to construct a 95% confidence interval for the average amount of 16 ounce bottles produced by the company. C= 95%, and a = 0.05, n= 30 for sample size. Using the calculator when came of the values +1.96 and -1.96. To come up with me margin of error, we multiply 1.96 by the standard deviation and divide by the square root of the sample size (30), which is 5.4772. The margin of error is then added and subtracted from the mean to give two numbers, the upper and lower. The values of upper and lower are 15.07 upper (rounded) and 14.67 lower. This means that we have a 95% confidence level that the sampling will be between 15.07 and 14.67. We are going to have to run two hypothesis tests, a null and an alternate. The null hypothesis is symbolized by H0. The alternate is symbolized using the H1. The company advertises that the soda bottles supposed to have 16 ounces of soda in them, but tests have shown the majority of the sampled bottles of less than 16. The hypothesis test will look like this:
H0- No bottle is less than 16 ounces
H1- A bottle is less than 16 ounces
Reject H0 in favor of H1
We know that because the employees measured 30 bottles of soda and found bottles less than 16 ounces, than H1 is true. Out of 30 samples, only two were equal or greater than 16 ounces. Since the majority of the bottles were under 16 ounces, each machine that produced less than 16 ounces need to be calibrated. The bottles may
Ron Hobson
Statistics
Professor Derrick Barbee
December 14, 2014
Bottle Company Case Study
Recently customers have complained that our soda bottles have not contained the 16 ounces of soda, which we advertise. To figure out the problem bottles were pulled randomly off of 30 machines. Our calculations concluded that there was a total of 446.1 ounces of soda measured from 30 bottles with an average (Mean) of 14.87 ounces of soda per bottle, with a mode of 14.8. The calculated standard deviation is 0.550329 Now we have to construct a 95% confidence interval for the average amount of 16 ounce bottles produced by the company. C= 95%, and a = 0.05, n= 30 for sample size. Using the calculator when came of the values +1.96 and -1.96. To come up with me margin of error, we multiply 1.96 by the standard deviation and divide by the square root of the sample size (30), which is 5.4772. The margin of error is then added and subtracted from the mean to give two numbers, the upper and lower. The values of upper and lower are 15.07 upper (rounded) and 14.67 lower. This means that we have a 95% confidence level that the sampling will be between 15.07 and 14.67. We are going to have to run two hypothesis tests, a null and an alternate. The null hypothesis is symbolized by H0. The alternate is symbolized using the H1. The company advertises that the soda bottles supposed to have 16 ounces of soda in them, but tests have shown the majority of the sampled bottles of less than 16. The hypothesis test will look like this:
H0- No bottle is less than 16 ounces
H1- A bottle is less than 16 ounces
Reject H0 in favor of H1
We know that because the employees measured 30 bottles of soda and found bottles less than 16 ounces, than H1 is true. Out of 30 samples, only two were equal or greater than 16 ounces. Since the majority of the bottles were under 16 ounces, each machine that produced less than 16 ounces need to be calibrated. The bottles may