Answer to Question #323794 in Statistics and Probability for secret

Question

According to Dietary Goals for the US (1977), high sodium intake may be related to ulcers, stomach cancer, and migrane headaches. The human requirement for salt is less than 220 milligrams per day, which is surpassed in most single servings of ready-to-eat noodles. If a random sample of 22 similar servings of noodles has a mean sodium content of 210 milligrams and a standard deviation of 5.23 does this suggest at the 0.01 level of significance that the average sodium content for a single servings of noodles is less than 220 milligrams?

Answer 1

$H_0:\mu \geqslant 220\\H_1:\mu <220\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{22}\frac{210-220}{5.23}=-8.96829\sim t_{n-1}=t_{21}\\P\left( T<-8.96829 \right) =F_{t,21}\left( -8.96829 \right) =6.29\cdot 10^{-9}\\The\,\,P-value\,\,is\,\,less\,\,than\,\,the\,\,significance\,\,level, \mu <220$