(a) Test the hypothesis Ho: σ² = 18 versus H₁: σ² + 18 using α = 0.05. Find the P-value for this test. (b) Suppose that the actual standard deviation is twice as large as the hypothesized value. What is the probability that this difference will be detected by the test described in part (a)? (c) Suppose that the true variance is oσ² = 40. How large a sample would be required to detect this difference with probability at least 0.90? 8-51. + The percentage of titanium in an alloy used in aero- space castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two- sided confidence interval for σ.