A manufacturer of light bulbs is considering a change in their supplier of tungsten for use in the bulbs' filaments. They believe this will result in bulbs that are "longer lasting." Currently, the lifetime of their bulbs, X, is a normally distributed random variable with population mean = 750 hours. After using tungsten from the new supplier for a production run, a random sample of 25 bulbs will be selected and the average lifetime of the bulbs will be computed. This result will be used to determine if there is sufficient evidence to conclude that the population mean lifetime of bulbs using this supplier is greater than 750 hours. The hypotheses are: Ho: 750 and Ha: > 750.

The production manager is concerned about the size of the sample used for the test. He decides to use a random sample of 100 bulbs using the new supplier's material and repeat the test described above with a level of significance of = .025. If it is true that using the new supplier results in bulbs that have a population mean lifetime of = 753.12 hours and standard deviation = 7.5 hours, which of the following statements is true? (Choose the most appropriate response.)

• A.The new sample will result in the conclusion to reject Hobecause it is false.
• B.The probability of a Type II error in this case is zero.
• C.The manager cannot make a Type I error in this case.
• D.The probability of a Type II error in this case is .0139.
• E.Both The manager cannot make a Type I error in this case and The probability of a Type II error in this case is .0139 are true.