Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST)

in Washington, D.C. Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams.

They weigh this weight on the scale 50 times and read the result each time. The 50 scale readings have a sample mean of x̄ = 1000.6 grams. The scale is out of calibration if the mean scale reading differs from 1000 grams. The technicians want to perform a hypothesis test to determine whether the scale is out of calibration.

a. State the appropriate null and alternate hypotheses.

b. The standard deviation of scale reading is known to be

σ = 2.

Compute the value of the test statistic.

c. State a conclusion. Use the α = 0.05 level of significance.