Question

Acid rain, caused by the reaction of certain air pollutants with rainwater, is a growing problem in the United States. Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity: 0 is acid; 14 is alkaline). Suppose water samples from 40 rainfalls are analyzed for pH, and x and s are equal to 3.2 and 0.9, respectively. Find a 99% confidence interval for the mean pH in rainfall. (Round your answers to three decimal places.)
______ to _______

Answer 1

Solution :

Given that,

= 3.2

s = 0.9

n = 40

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* (s /n)

= 1.96 * (0.9 / 40)

= 0.279

At 99% confidence interval estimate of the population mean is,

- E < < + E

3.2-0.279 < < 3.2+0.279

2.921< <3.479

2.921 to 3.479