Question #329317

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.


1
Expert's answer
2022-04-19T03:28:18-0400

H0:μ=77H1:μ77Z=nxˉμσ=n657744=0.272727nz1+γ2=z0.975=1.960H0isrejectedif0.272727n>1.960n>(1.9600.272727)2=51.6483H_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


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