20. The weekly proportion of storage tank capacity that is utilized at a regional hazardous liquid waste receiving site is an outcome of a Beta(y,1) random variable. At the end of each week the storage tank is emptied. A random sample of a year’s worth of observations of capacity utilization at the site produced the results displayed in the table below, reported in sequence row-wise.

(a) Define a GLR size a test of H0: y ¼ y0 versus H0: y 6¼ y0.

(b) Test the hypothesis that the expected weekly storage tank capacity utilized is equal to .5 at a significance level of .95. If the exact distribution of the GLR test appears to be intractable, then use an asymptotic test.

(c) Test that the observations can be interpreted as a random sample from some population distribution.

Use a size .05 test