Questions:
1 An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 7.9 lbs/square inch. The valve was tested on 240 engines and the mean pressure was 8.0 lbs/square inch. Assume the standard deviation is known to be 0.8. Is there evidence at the 0.05 level that the valve performs above the specifications?
2 A local police chief claims that less than 60% of all drug-related arrests are ever prosecuted. A sample of 800 arrests reveals that 56% of arrests were prosecuted. Is there sufficient evidence at the 0.02 level to substantiate the chief's claim?
3 A lumber company is making boards that are 2756.0 millimeters tall. If the boards are too long they must be trimmed, and if they are too short they cannot be used. A sample of 28 boards is made, and it is found that they have a mean of 2760.2 millimeters with a variance of 121.00. Is there evidence at the 0.05 level that the boards are either too long or too short? Assume the population is normally distributed.