Answer to Question #329317 in Statistics and Probability for nini

Question

The average value of the particulate matter (PM10) in the air of Kuala Lumpur is 77 (μg/m3).. The average value of the particulate matter (PM10) is 65 (μg/m3) as calculated from the sample data. The standard deviation of the population is 44 (μg/m3). Use a significance level of α=0.05 to carry out the analysis.

Answer 1

$H_0:\mu =77\\H_1:\mu \ne 77\\Z=\sqrt{n}\frac{\bar{x}-\mu}{\sigma}=\sqrt{n}\frac{65-77}{44}=-0.272727\sqrt{n}\\z_{\frac{1+\gamma}{2}}=z_{0.975}=1.960\\H_0\,\,is\,\,rejected\,\,if\\0.272727\sqrt{n}>1.960\Rightarrow n>\left( \frac{1.960}{0.272727} \right) ^2=51.6483$