Question: A sample of 80 fluorescent bulbs is tested to check the hypothesis that the mean life
, as claimed by the manufacture is at least 750 hours. If the population standard deviation is 68 hours can we conclude at 95% confidence that the mean life of the fluorescent bulbs is less than 750 hours?  Edit

Answer: Standard Error = 68/sqrt(80) = 4.25
Let the sample mean be m
Test Statistic = T = (m - 750)/4.25
The test statistic follows a t-distribution with degrees of freedom (80 - 1) = 79
Now, the critical value for the test is - 1.99
If the observed value of the t is less than this level, we might conclude that the mean life of the fluorescent bulbs is less than 750 hours; otherwise not.  Edit