2. Two types of valves are being tested to determine if there is a difference in pressure tolerances. Fifteen out of a random sample of 100 of Valve A cracked under 4,500 psi. Six out of a random sample of 100 of Valve B cracked under 4,500 psi. Test at a 5% level of signicance for a difference in pressure tolerance between the two types of valves. {a} Test at a 5% level of significance for a difference in pressure tolerance bemeen the two types of valves. [14] {b} Calculate a 95% confidence interval for a difference in proportions of valves that cracked between type A and type B. Is this result in agreement with the conclusion at point {a}. [4] {c) For the question 4 above the data can be summarised in the following 2x2 contingency table Pressure tolerance cracked Valve A 1 Valve B At the 5% level of signicance test for an association between valve type (MB) and pressure tolerance {crackedfnot cracked]. |Compare the result to the one obtained under point {a). [12]