Question

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 significance.

Answer 1

Total number of sample 1 (n1) = 100
Total number of sample 2 (n2) = 100
number of favourable events (X1) = 15
number of favourable events (X2) = 6

We are interested in testing the hypothesis

Since, the test is two-tail test at \alpha = 0.05

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.959963984540054 or greater than the critical value 1.959963984540054
The statistic value, 2.076 is greater than the critical value 1.959963984540054. Hence, reject the null hypothesis.