Question: Delivery department of a manufacturing company A&B uses a company CDE for its shipping needs. CDE have delivered their shipments on schedule (on or before the scheduled delivery date) 85% of the time in the past. A&B believes that on time delivery is a key to their customer satisfaction and continued loyalty. If the on time delivery rate of CDE is less than 85%, A&B will have to consider other shippers or alternative options. A&B collects a random sample of size 625 from their shipments across a year and finds that 515 shipments were delivered on time.

1. State the appropriate null and alternate hypotheses to test.
2. Find the standard error, the test statistic, and the p-value.
3. Is there significant evidence at level 1% to believe that the on time delivery of CDE is less than 85%?
4. Is there significant evidence at level 5% to believe that the on time delivery of CDE is less than 85%?
5. Find the 99% confidence interval for the proportion of time CDE delivers the shipments on time.
6. In order to explore their options, another random sample of 625 shipments across a year were sent via a different shipping carrier FGH. 530 of those shipments were delivered on time. Is the performance of FGH significantly better than that of CDE? Calculate the appropriate test statistic to answer this question and find the p-value.
7. Based on the calculations in f, is the performance of FGH significantly better than that of CDE at level 5%?
8. Find the 99% confidence interval for the difference between the proportions of on time delivery by CDE and by FGH.

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