A new light bulb is being considered for use in an office with computers. It is decided that the new bulb will only be used if it has a mean lifetime of more than 500 hours. A random sample of 40 bulbs is selected and placed on life test. The mean and standard deviation are found to be 505 hours and 18 hours, respectively. Perform the appropriate test of hypothesis to determine whether the new bulb should be used.
Which is the correct null and alternate hypothesis?
a) Ho: xbar=505 vs. Ha: xbar>505
b) Ho: mu=505 vs. Ha: mu>505
c) Ho: xbar=500 vs. Ha: xbar>500
d) Ho: mu=500 vs. Ha: mu>500
Explain your conclusion.