The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, mu, is close to the target fill of 16 ounces. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 16 ounces, then the fillers initial setup will be readjusted.
a: The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test.
b: Suppose that Crown Bottling Company decides to use a level of significance of alpha = .01, and suppose a random sample of 36 bottle fills is obtained from a test run of the filler. For each of the following four sample means x-bar = 16.05, x-bar = 15.96, x-bar = 16.02,and x-bar = 15.94 determine whether the fillers initial setup should be readjusted. In each case, use a critical value, a p-value, and a confidence interval. Assume that s equals .1.
The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.