Question

UFG rents the flatbed trailers on which the organizations participating in the Gainesville 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 56 lb. The types of floats used in the Gainesville parade typically fall into the second classification on the company’s pricing scale. This classification places an upper limit of 1000 lb on the mean. Therefore UFG wishes to perform the following hypothesis test (using a level of significance of 0.05). where mu denotes the mean weight of a parade float. Furthermore, UFG wishes to detect a true mean of 1,026 lb with a probability of 0.90. What is the appropriate sample size for this test?

Answer 1

H0: $\mu$ = 1000 lb

Ha: $\mu$ < 1000 lb

z value for p=0.90 is 1.28

Standard error of the mean = SD / $\sqrt{n}$    where n is the sample size.

= 56 / $\sqrt{n}$

Thus,

1.28 = (1026 - 1000) / (56 / $\sqrt{n}$ )

=> $\sqrt{n}$ = 1.28 * 56 / 26

=> $\sqrt{n}$ = 2.756923

=> n = 7.6

So, the appropriate sample size for this test is 8.