The diameter of a spindle in a small motor is supposed to be 5 millimeters with a st.dev. of 0.04 mm. If the spindle is either too small or too large, the motor will not perform properly. The manufacturer measures the diameter in a sample of 10 motors and finds the average to be 5.04 mm. Does the manufacturer have significant evidence ( alpha = .01) that the shipment of motors is defective?
1. Define the population, variable, and parameter you will use.
2. State the hypotheses. State the level of significance.
3. Name the test.
4. Conduct the test giving statistics, the test statistic and the P-value. ( Show your work )
5. Write a conclusion that answers the question.
6. Find a 95% confidence interval.
7. What type of error could we have made in our conclusion?