Read Chapter 4
Problems:
1. A turning operation is used to manufacture shafts. The manufacturer claims that the mean diameter of the shafts produced by the process is 20.5 mm. Prior study of the process has revealed that the shaft diameters are normally distributed with a standard deviation of 0.5 mm. Answer the following questions assuming an α risk level of 0.05.
a. A randomly selected shaft is selected, and its diameter is measured to be 21.2 mm. Using the step-by-step procedure described in class, conduct a statistical test of hypothesis to evaluate the manufacturer’s claim based on this single value.
b. A group of six shafts are selected; the sample mean diameter of this group of shafts is calculated to be 19.8 mm. Using the step-by-step procedure described in class, conduct a statistical test of hypothesis to evaluate the manufacturer’s claim based on this sample mean value.
2. The level of inhalable airborne particulate within a production facility is claimed to be 0.5 mg/m3 on the average. Previous investigations have revealed that air quality measurements are normally distributed with a standard deviation of 0.1 mg/m3. Answer the following questions assuming an α risk level of 0.02.
a. A single air quality measurement is taken in the plant – 0.27 mg/m3. Conduct a statistical test of hypothesis to evaluate the claim based on this single value.
b. Four air quality measurements are taken in the plant over the course of one shift – the sample mean of the measurements is calculated to be 0.55 mg/m3. Conduct a statistical test of hypothesis to evaluate the claim based on this sample mean value.
3. A bakery shop advertises that their cookies have an average mass of 150 grams. The distribution of individual cookie masses is known to be normal with a standard deviation of 20 grams. A consumer protection group has decided to monitor the shop’s claim. They would like some “automated” procedure to periodically check the mass of a cookie, compare the measured mass to lower and upper rejection limits (XL and XU values), and then make a decision about whether to confront/not confront the shop about their advertising.
a. Assuming an α risk value of 0.05, find the values for XL and XU.
b. What is the β risk for a true mean cookie mass of 130 grams?
c. Calculate the β risk for a range of true mean cookie masses. Prepare a graph that displays the probability of passing the rejection criterion as a function of the true mean cookie mass (the operating characteristic curve).
Graduate Credit:
1) Formulate one new problem each for chapter1, 2, 3, 4 and one on Hypothesis Testing.
2) Solve the problems.
3) Submit the formulation and the solution.
Please be innovative in formulating the new problems. They should be different from the one given in the book.
Problems?? contact psshirod@mtu.edu