The titanium content in an aircraft-grade alloy is an important determinant of strength. A sample of 20 test coupons reveals the following titanium content (in percent):

8.32, 8.05, 8.93, 8.65, 8.25, 8.46, 8.52, 8.35, 8.36, 8.41, 8.42, 8.30, 8.71, 8.75, 8.60, 8.83, 8.50, 8.38, 8.29, 8.46 The median titanium content should be 8.5%.

(a) Use the sign test with 0.05 to investigate this hypothesis. Find the P-value for this test.

(b) Use the normal approximation for the sign test to test versus , with 0.05. What is the P-value for this test?