A consumer agency suspects that a pet food company may be under filling packages for one of its brands. The package label states “1600 grams net weight,” and the president of the company claims the average weight is at least 1600 grams. For a simple random sample of 35 boxes collected by the consumer agency, the mean and standard deviation were 1591.7 grams and 18.5 grams, respectively.
a. At the 0.05 level of significance, what conclusion should be reached by the consumer agency? Would the president of the company prefer to use a different level of significance in reaching a conclusion? Explain.
b. Use the decision rule associated with part (a) and a range of selected assumed values for μ in constructing the power curve for the test.