The paint used to make lines on roads must reflect enough light to be clearly visible at night.Letdenote the true average retroreflectance (brightness) for a new type of paint under consideration.Any paint used must have a brightness of at least 20 reflectance units.A sample of=56paint markings were tested, and the sample mean and standard deviation were-=20.5 and=3 reflectance units respectively.We want to determine whether this brand of paint is bright enough to be used.

a.Calculate the rejection region for a significance level of=0.05. Report your answer in terms of the test statistic ( subscript())orsubscript()as appropriate), and also in terms of-.

b.Compute the value of the test statistic from the data given.

c.Determine theP-value of your hypothesis test, and state the result of the test.