The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to...

The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials. Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a 0.10 level of significance.

(a) Calculate the pooled estimate of the population proportion.

(b) Compute the value of the test statistic.