The dean of instruction at a local college requested that a new standardized test for an introductory statistics course be developed with the requirement that it should have µ = 100 and σ = 10. a class of 30 students complete the new test with a mean grade of 95. conduct a hypothesis test at α = .05 to determine whether the claim that µ = 100 can be supported. use the p-value approach and complete the following to show how this would be done.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?