It is desired to check the calibration of a scale by weighing a standard 10 g weight 100

Chapter 6, Problem 11

(choose chapter or problem)

It is desired to check the calibration of a scale by weighing a standard \(10 g\) weight 100 times. Let \(\mu\) be the population mean reading on the scale, so that the scale is in calibration if

\(\mu=10\). A test is made of the hypotheses \(H_{0}: \mu=10 \text { versus } H_{1}: \mu=10\). Consider three possible conclusions: (i) The scale is in calibration. (ii) The scale is out of calibration. (iii) The scale might be in calibration.

a. Which of the three conclusions is best if \(H_{0}\) is rejected?

b. Which of the three conclusions is best if \(\(H_{0}\)\) is not rejected?

c. Is it possible to perform a hypothesis test in a way that makes it possible to demonstrate conclusively that the scale is in calibration? Explain.

Equation Transcription:

   

       

       

   

   

Text Transcription:

10 g

\mu

\mu=10

H_{0}: \mu=10 versus  H_{1}: \mu=10

H_{0}

H_{0}