Bottling Company Case Study
Introduction to Statistics: MAT 300
Recently customers have begun to complain that the bottles of the brand of soda produced in this company contains less than the advertised 16 ounces of product. I have pulled 30 bottles of soda and am calculating the mean, median, standard deviation, constructing a 95% confidence interval and conducting a hypothesis test to verify the claim that a bottle contains less than 16 ounces is supported.
The first set of tests will consist of calculating the mean, median and standard deviation for ounces in the bottles. Below is the data set from the 30 bottles collected:
Bottle Number | Ounces | Bottle Number | ...view middle of the document...
045 & 2.045, test statistic of 0.428. The two critical values were calculated by performing a t calculation of the level of significance of .05 using degrees of freedom of 29. Since we are finding two critical values, divide the level of significance by 2 (.025) and use the degrees of freedom to calculated the critical values. To find the test statistic, use the mean, standard deviation, expected value and degrees of freedom.
Since the test statistic is less than the critical value, then we fail to reject the null hypothesis. Through the tests, I have concluded that there are less than 16 ounces in a bottle of soda and there are a few possible causes. We will review the possible causes and strategies to avoid the deficit in the future.
One possible cause to the deficit of soda in the bottles is the calibration of the machine that fills up the soda bottles. This is the most likely cause overall as the difference in largest filled bottle and lowest filled bottle is 2.1 ounces. The...