In: Statistics and Probability
An Izod impact test was performed on 20 specimens of PVC pipe. The ASTM standard for this material requires that Izod impact strength must be greater than 1.0 ft-lb/in. The sample average and standard deviation obtained were x over Bar = 1.121 and s = 0.328, respectively. (a) Test the hypothesis that σ2 = 0.10 against an alternative specifying that σ2 ≠ 0.10, using α = 0.01 (if reject enter a value of 1, if not, enter a value of 2). (b) What is lower bound and upper bound of P-value for this test? Round your answers to 1 decimal place. Answers are exact. (c) Find a 99% two-sided CI for σ2: lower bound and upper bound. Round your answers to 3 decimal places. (d) Use the confidence bound in the previous part to test the hypothesis (if reject enter a value of 1, if not, enter a value of 2).
a)
The test statistic is
= 20.44
df = 20 - 1 = 19
At = 0.01, the critical values are
6.844
38.582
Since the test statistic value lies between the critical values, so we should not reject the null hypothesis.
b) P-value = 2 * P( > 20.44)
= 2 * 0.3686
= 0.7372
P-value > 0.5
c) The 99% confidence interval for is
Lower bound = 0.053
Upper bound = 0.299
d) Since the confidence interval contains 0.1, so we should not reject the null hypothesis.