4. A factory manufactures treadmills and has a warranty of 5 years on their products. An engineer at the factory believes that the treadmills do not last that long and will malfunction in less than 5 years.
He tests a sample of 40 treadmills and find the average time to be 4.8 years with a standard deviation
of 0.50. (5 points)
a. State the null and alternative hypotheses
b. At the 95% confidence level, is there enough evidence to support the engineer's claim?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?