The operations manager at a light bulb factory wants to determine whether there is a difference in the average life expectancy of bulbs manufactured on two different types of machines. The process standard deviation of Machine I is 110 hours and of Machine II is 125 hours. A random sample of 25 lights bulbs obtained from Machine I indicates a sample mean of 375 hours and a similar sample of 25 from Machine II indicates a sample mean of 362 hours. Using the 0.05 level of significance, which of the following statements offers the most accurate and appropriate measure that there is not enough evidence to conclude that there is a difference in the average life of bulbs produced by the two types of machines?
A. Z = 0.3904 and is between the critical bounds of + 1.96
B. t = 0.0117 and is between the critical bounds of + 2.01
C. t = 1.3829 and is between the critical bounds of + 2.01
D. Z = 0.424 and is between the critical bounds of + 1.96
This solution provides equations and explanations for determining a difference in means.