Answer to Question #314435 in Statistics and Probability for Rahul

Question

We wish to know if we can conclude that the mean daily caloric intake in

the adult rural population of

a developing country is less than 2000. A sample of 500 had a mean of 1985

and a standard deviation

of 210. Let alpha = 0.5

Answer 1

$H_0:\mu \geqslant 2000\\H_1:\mu <2000\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{500}\frac{1985-2000}{210}=-1.59719\sim t_{n-1}=t_{499}\\P-value:\\P\left( T\leqslant -1.59719 \right) =F_{t,499}\left( -1.59719 \right) =0.0554$

Since the P-value is less than the significance level, the null hypothesis is declined. The mean value is less than 2000.