Question 1194137
assumed population mean = 36000
sample mean = 32940
population standard deviation = 1950
sample size = 28
standard error = 1950/sqrt(28) = 368.52
z-score= (32940 - 36000) / 368.52 = -8.30
the probability of getting a z-score less than or equal to -8.30 by random chance = 0.
this suggests that the average lifetime of the bulbs is more then likely less than 36000.
at 0.5% significance level, the critical z-score would be equal to -2.57
-8.30 is much greater than that.
this supports the conclusion that the average lifetime of the bulbs is more than likely less than 36000 hours.
the standard error represents the standard deviation of the distribution of a large number of sample means from samples that all have 28 elements in them.
let me know if you have any questions.
theo