Example 1
A pharmaceutical manufacturer does a chemical analysis to check thepotency of products. The standard release potency for cephalothincrystals is 910. An assay of 16 lots gives the following potencydata:
897 914 913 906 916 918 905 921 918 906 895 893 908 906 907901
Assume the population standard deviation is 8 units. Test thehypothesis that the population mean potency is different from thestandard release potency.
(1) Define the population quantity of interest in this study.This is called the population parameter.
(2) Carefully state the hypotheses to be tested about thepopulation.
(3) What is the sample size?
(4) What quantity will be used as an estimate of the parameter from(1)? (5) What is the distribution of the sample estimate?Why?
(6) What is the standard deviation of the sample estimate?
(7) What is the value of the sample estimate for the sample in thisstudy? (8) Find the test statistic. What does this measure?
(9) Give the p-value for the test in (2). What does thismeasure?
(10) Carefully state your conclusions.
(11) What assumptions have we made for this procedure to bevalid?
