In: Math
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 __
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)