USFEC rents the flatbed trailers on which the organizations participating in the parade build their floats. The company that owns these trailers determines their rental price based on the mean weight of a parade float. The standard deviation of float weight is widely known to be 125 pounds. The types of floats used in the Martinsville parade typically fall into the second classification on the company's pricing scale. This classification places an upper limit of 850 pounds on the mean. Therefore, USFEC wishes to perform hypothesis test about the mean weight of a parade float using a level of significance of 0.1. Furthermore, USFEC wishes to detect a true mean of 900 pounds with probability 0.95.
(a) What sample size should USFEC use?
(b) State the null and alternative hypothesis. What is the critical region for this test?
(c) What is the power of this test if the true mean float weight is 885 pounds?
(d) If the sample size computed in part (a) is used and the resulting sample mean is 868 pounds, then what is the value of the test statistic and the corresponding conclusion for the test?
(e) What is the smallest level of significance that would have resulted in rejecting the null hypothesis?