Question

A manufacturer of irrigation systems for buildings claimed that their systems are activated at an average temperature of a 130 degrees Fahrenheit, but affected customers claim that the systems have not been activated for a while and conclude that the average activation temperature is greater than the one claimed by the manufacturer, which puts people's lives at risk. 9 systems were tested and the average activation temperature was 131.8 degrees. If we assume that the activation temperature follows a normal distribution with a known variance of 1.5 degrees:

a) If the manufacturer's claim is true and the reaction temperature is indeed 130 degrees, what will be the probability of concluding that it is false?

b) If the manufacturer's claim is true, what proportion of the systems will not activate until the temperature reaches a value greater than 130 degrees?

c) A colleague of yours with very little exposure to statistical concepts determines that you will do the test simply by testing 10 systems at random and that you will conclude that the average activation temperature is greater than 130 degrees if the average of the 10 observations is equal to or greater than 130.5 degrees. How likely is this test to make a Type I error?

Answer 1