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1. (18.10) Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that...

1. (18.10) Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain." The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a Canadian forest follow a Normal distribution with standard deviationσ= 0.5. A sample ofndays finds that the mean pH isx= 4.8.

Give a 80 % confidence interval for the mean pH μ when n = 5, n = 15, and n = 40

n= 5 ____to ____

n= 15__ to ___

n= 40 __ to __

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 4.8

Population standard deviation =    = 0.5

1) Sample size = n = 5

At 80% confidence level

= 1 - 80%  

= 1 - 0.80 =0.20

/2 = 0.10

Z/2 = Z0.10 = 1.282


Margin of error = E = Z/2 * ( /n)

= 1.282 * ( 0.5 /  5 )

= 0.29

At 80% confidence interval estimate of the population mean is,

  ± E

4.8 ± 0.29

( 4.51 , 5.09)  

2)  n = 15

Margin of error = E = Z/2 * ( /n)

= 1.282 * ( 0.5 /  15 )

= 0.17

At 80% confidence interval estimate of the population mean is,

  ± E

4.8 ± 0.17

( 4.63 , 4.97)

3) n = 40

Margin of error = E = Z/2 * ( /n)

= 1.282 * ( 0.5 /  40 )

= 0.10

At 80% confidence interval estimate of the population mean is,

  ± E

4.8 ± 0.10

( 4.70 , 4.90)


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