Question

Noise levels at 3 airports were measured in decibels yielding the following data:

Answer 1

Answer:

a)  The 90% confidence interval for the mean noise level at such locations      

  (112.46 , 163.54)

b) The critical value that should be used in constructing the confidence interval

Z₀.₁₀ = 1.645

Step-by-step explanation:

Step(i) :-

Noise levels at 3 airports were measured in decibels yielding the following data

108   146   160

Mean of given data

         $x^{-} = \frac{108+146+160}{3} = 138$

x          :     108   146   160

x-x⁻      :      -30   8       22

(x-x⁻ )² :     900   64     484

Variance  σ ² = ∑(x-x⁻ )²/ n-1

                                        = $\frac{900+64+484}{3-1}= 724$

Standard deviation  

                σ = √724 = 26.90

Step(ii):-

The 90% confidence interval for the mean noise level at such locations                        

       $(x^{-} - Z_{0.90} \frac{S.D}{\sqrt{n} } , (x^{-} + Z_{0.90} \frac{S.D}{\sqrt{n} } )$

The critical value that should be used in constructing the confidence interval

Z₀.₁₀ = 1.645

         $(138 - 1.645 \frac{26.90}{\sqrt{3} } , (138 + 1.645 \frac{26.90}{\sqrt{3} } )$

        ( 138 - 25.54 , 138 + 25.54 )

        (112.46 , 163.54)