Question

A series of tests of fire prevention sprinkler systems that use a foaming agent to quell the fire were performed to determine how long it took (in seconds) for the sprinklers to be activated after the detection of a fire by the system. The system has been designed so that the true average activation time is supposed to be at most 25 seconds. Do the data strongly indicate that the design specifications have not been met?

The data for the test are given below:
27 41 22 27 23 35 30
33 24 27 28 22 24

Answer 1

No, they do not.

Explanation:

To determine whether or not the design specifications have been met, you need to find the average of all of the times and see if it lines up with the intended one.
`(27+41+22+27+23+35+30+33+24+27+28+22+24)/(13)=(363)/(13)\approx 27.92` seconds. This is within one standard deviation of the desired time, meaning that the data suggests that the design specifications have been met. Hope this helps!