A company manufactures electric bulbs and claims that the average lifetime of bulbs is 1200 hours.

A quality inspector suspects that the actual mean lifetime is different.

To test this, a large sample of 100 bulbs is selected. The sample mean lifetime is 1185 hours, and the population standard deviation is known to be 60 hours.

The company also compares two production units:

• Unit A: sample size = 80, mean = 1190 hours
• Unit B: sample size = 70, mean = 1210 hours
• Standard deviations are assumed equal and known.

Z-Test (Large Sample Test)

a) Compute the Z-test statistic using:

• Population mean = 1200
• Sample mean = 1185
• σ = 60
• n = 100

b) Write the formula used for Z-test.
c) At 5% level of significance (Z critical = 1.96), state whether H᐀ is rejected or accepted.