An air conditioning company servicing a certain machine roomguarantees that the temperature in the room stays below 20o C. Dueto malfunctioning of the equipment operating in the machine room,it is suspected that the average temperature actually exceeds 20ofor more or less extended periods of time. Seven temperaturemeasurements are collected throughout the day and the followingtemperatures are observed, 20.8, 20.2, 20.9, 21.5, 22.2, 21.2,19.8. Assuming that the temperature is at least approximatelynormally distributed,
a) can you say at a 5% significance level that the roomtemperature is actually above 20o C?
b) what is the (approximate) p-value for this test? What does ittell you about the conclusion you have just made regarding the roomtemperature?
c) What is the probability that this test fails to reject Hoeven though the true mean temperature is 21o C?
