Recall the sugar content of the syrup in canned peaches from Exercise 8-51. Suppose that the variance is thought to be σ² = 18 (milligrams)². Recall that a random sample of n = 10 cans yields a sample standard deviation of s = 4.8 milligrams. 

(a) Test the hypothesis H₀: 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 σ² = 40. How large a sample would be required to detect this difference with probability at least 0.90?