Question

A cement manufacturer claims that the average weight of his product is 40 kg: with a standard deviation of 2.35 kg A sample of 45 bags was taken and found to have a mean weight of 38.71 kg: Are we going to accept the claim of the cement manufacturer? Use 0.01 level of significance

Answer 1

$H_0:\mu =40\\H_1:\mu \ne 40\\Z=\sqrt{n}\frac{\bar{x}-\mu}{\sigma}=\sqrt{45}\frac{38.71-40}{2.35}=-3.68238\\P\left( \left| Z \right|>3.68238 \right) =2\varPhi \left( -3.68238 \right) =2\cdot 0.00012=0.00024<0.01\Rightarrow \\\Rightarrow H_0\,\,is\,\,rejected$