Question

A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is approximately normally distributed. A random sample of 15 rings has a mean diameter of x ̅=74.036 mm with a standard deviation of 0.02 mm.

(a)   Test the hypothesis that the mean piston ring diameter is 74 mm using the P-value method. Use α = 0.01.

(b)   Construct a 99% two-sided confidence interval on the mean piston ring diameter.

(c)   Construct a 95% lower-confidence limit on the mean piston ring diameter.

Answer 1

Solution: We are given:

(a)   Test the hypothesis that the mean piston ring diameter is 74 mm using the P-value method. Use α = 0.01.

Answer: The null and alternative hypotheses are:

The test statistic is:

  

Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude the mean piston ring diameter is not 74 mm

(b)   Construct a 99% two-sided confidence interval on the mean piston ring diameter.

Answer: The 99% confidence interval is:

(c)   Construct a 95% lower-confidence limit on the mean piston ring diameter.

Answer: The 95% lower-confidence limit on the mean piston ring diameter is: