Question

An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 19 water samples and measure their pH level. The mean and standard deviation are 6.5 and 0.25, respectively. Is there enough evidence to reject the company’s claim at a significance level of 0.05?

Answer 1

$H_0:\mu =6.8\\H_1:\mu \ne 6.8\\\\T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{19}\frac{6.5-6.8}{0.25}=-5.23068~t_{n-1}=t_{18}\\P-value:\\P\left( \left| T \right|>5.23068 \right) =2F_{t,18}\left( -5.23068 \right) =2\cdot 2.83\cdot 10^{-5}=5.66\times 10^{-5}$

Since the P-value is less than the significance level, the null hypothesis is rejected, the PH level differs from 6.8.