Question

9.) 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 of n days finds that the mean pH is x= 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 ___

Answer 1

(a)

= 4.8

= 0.5

n = 5

=0.20

From Table, critical Values of Z = 1.282

Confidence Interval:

So,

Answer is:

n = 5:    4.513 to 5.087

(b)

= 4.8

= 0.5

n = 15

=0.20

From Table, critical Values of Z = 1.282

Confidence Interval:

So,

Answer is:

n = 15:    4.635 to 4.965

(c)

= 4.8

= 0.5

n = 40

=0.20

From Table, critical Values of Z = 1.282

Confidence Interval:

So,

Answer is:

n = 40:    4.699 to 4.901