Question

A youngathlete wishes to test if the average cost of men's athletic shoes is less than P4000 compared to the claim that it is at least P4 000. He selects a sample of 36 pairs of shoes from a catalog and finds the average cost to be P3 790. The standard deviation of the population is P660. What is the probability of committing a type I error

Answer 1

$H_0:\mu \geqslant 4000\\H_1:\mu <4000\\Z=\sqrt{n}\frac{\bar{x}-\mu}{\sigma}=\sqrt{36}\frac{3790-4000}{660}=-1.90909\\\alpha =P_{H_0}\left( Z\leqslant -1.90909 \right) =\varPhi \left( -1.90909 \right) =0.0281$