Emissions of sulfur dioxide by industry set off chemical changes in the atmosphe

Question

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 deviation = 0.4.

A sample of n days finds that the mean pH is x = 4.8. Give a 95% confidence interval for the mean pH when

n = 64.

______ to ______

Explanation / Answer

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    4.8          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    0.4          
n = sample size =    64          
              
Thus,              
Margin of Error E =    0.097998199          
Lower bound =    4.702001801          
Upper bound =    4.897998199          
              
Thus, the confidence interval is              
              
(   4.702001801   ,   4.897998199   ) [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.