Question

Calibrating a scale: 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. The standard deviation for scale reading is known to be o = 3.1. They weigh this weight on the scale 45 times and read the result each time. The 45 scale readings have a sample mean of x = 999.4 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. Use a = 0.01 level of significance and the critical value method. Part: 0/5 Part 1 of 5 (a) State the appropriate null and alternate hypotheses. HO H: This hypothesis test is a (Choose one) test.

Answer 1

HO: =1000 H1:u #1000 (Two tailed) Population mean = u = 1000 Population S.D = 0 =3.1 Sample size = n =45 Sample mean = x = 999.4

Significance Level = a = 0.01 Using Excel Critical value=z*= ABS(NORM.S.INV(0.01/2)) = 2.58 Thus the critical values for two tailed test are -2.58 and 2.58. Decision Rule: "Reject Ho if z<-2.58 or z> 2.58."

The test statistic is, N-U 2 = = (999.4 - 1000)/(3.1/N45) = -1.3 아들

Conclusion : By decision rule, we fail to reject HO