Demonstrating the steps in hypothesis testing
Solve as indicated. Show the steps in hypothesis testing.
- A manufacturing company has been averaging 18 orders per week for several years. However, during the recession, orders appeared to slow. Suppose the firm's production manager randomly samples 35 weeks and finds a sample mean of 16 orders. The population standard deviation is 2.5 orders. Is there reason to believe that a decline in the number of orders per week has occurred? Use 5% level of significance.
- A manufacturer packs sugar into plastic bags. Each bag contains two kilograms of sugar. When the production process is under control, each bag will contain on the average two kilograms. To check the process, a random sample of 25 bags was chosen and showed a mean of 2.2 kilograms and a standard deviation of 0.12 kilogram. Can the manufacturer conclude that the process is under control? Use 5% level of significance.
- A large manufacturing company investigated the service it received from suppliers and discovered that in the past, 32% of all materials shipments were received late. However, the company recently installed a just-in-time system in which suppliers are linked more closely to the manufacturing process. A random sample of 110 deliveries since the just-in-time system was installed reveals 24 deliveries were late. Using 5% level of significance, can you conclude that the system has significantly reduced late deliveries?