The Air Pumps at Service Stations Come Equipped with a Gauge

Essay

The air pumps at service stations come equipped with a gauge to regulate the air pressure of tires.A mechanic believes that the gauges are in error by at least 3 pounds per square inch.To test his belief he takes a random example of 50 air pump gauges and determines the difference between the true pressure (as measured by an accurate measuring device)and the pressure shown on the air pump gauge.The mean and the standard deviation of the sample are $\bar { x }$ = 3.4 and s = 1.2.Can the mechanic infer that he is correct at the 5% significance level? Assume tire pressures have a normal distribution.