A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 30 ounces. The distribution of weights is known to be normal, with standard deviation . A random sample of boxes yielded an average weight of ounces. Suppose an inspector wants to test the null hypothesis that the population mean weight is at least 30 ounces. That is, test the null hypothesis
against the alternative hypothesis
Answer the following, rounding off your answers to two decimal places.
(a)
What is the test statistic used in the decision rule?
(b)
What is the critical value the inspector will use? Use a 10% level of significance.
(c)
What decision do you make?
A.
Do not reject the null hypothesis.
B.
Reject the null hypothesis.
You can earn partial credit on this problem.