Due to late delivery problems with an existing supplier, the director of procurement at Electro Tech began to place orders for electrical switches with a new supplier as part of a "dual-source" (two-supplier) strategy. Now she wants to revert to a "single-source" (i.e., one supplier) strategy to simplify purchasing activities. She wishes to conduct a test to infer whether the new supplier will continue to outperform the old supplier. Based on recent sample data, she found that 27 of 150 orders placed with the old supplier arrived late, whereas 6 of 75 orders placed with the new supplier arrived late.
a. Specify the null and alternative hypotheses to test for whether the proportion of late deliveries with the new supplier is less than that of the old supplier.
b. Compute the value of the test statistic.
c. Use the critical value approach to test the hypotheses at the 5% significance level. What is the conclusion?