Statistics question Need help? A bottling beer bottle labels for a particular type of beer containing 330 ml of beer. To err on the side secure, it is actually intended to put an average of at least 335ml of beer in each bottle. Each time a new batch of bottles is started bottling machine must be reset, and therefore the average contents of cylinders must be checked. A sample of 60 bottles is checked at the beginning of each batch. If this sample provides evidence that the average content is less than 335ml, the process is stopped and the material filling is set. For the sample of the latest batch of content mean is 332ml, and the standard deviation is 10 ml.
(A) Calculate a confidence interval of 95% for the contents of the bottle means in the last series.
(B) propose and implement an appropriate statistical test for the last batch, stating clearly the null and alternative hypotheses. Justify your choice test. Use a significance level of 5%. Enter your conclusion clearly in layman (that is, statistical) terms.
(C) If the same standard deviation and average was obtained from a sample of 20 bottles (instead of 60) retest your assumptions. Clearly all the additional assumptions that you made.
(D) Using the statistical test in part (b) what is the probability that the bottling process is stopped for adjustment when the lot is in fact the realization of its objective content of the average bottle of 335ml?
(E) Calculate the power of statistical test used in part (b) if the true average for the lot was 329.5ml and true standard deviation is 9.5 ml. Sketch the shape of the power curve of scoring known to you. What you say about the chances that the bottling company is actually "cheating" its customers in a particular lot without realizing it?
Thank you
Jammy Badger oi you make yourself like the rest of us!
no0b
Posted on May 26, 2010.
