1. A company wants to test a randomly selected sample of n water specimens and estimate the mean daily rate of pollution produced by a mining operation. If the company wants a 95?% confidence interval estimate with a margin of error of 1.2 milligrams per liter? (mg/L), how many water specimens are required in the? sample? Assume prior knowledge indicates that pollution readings in water samples taken during a day are approximately normally distributed with a standard deviation equal to 6 ?mg/L.
The company must sample ???? water specimens in order to estimate the mean daily rate of pollution produced by a mining operation to 1.2 ?mg/L with 95?% confidence.
2. The mean and standard deviation of a random sample of n measurements are equal to 33.1 and 3.7?, respectively.
a. Find a 95?% confidence interval for μ if n=49.
b. Find a 95?% confidence interval for μ if n=196.
c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient? fixed?
a. The 95?% confidence interval for μ if n=49 is approximately ( , ).
?(Round to three decimal places as? needed.)
b. The 95?% confidence interval μ if n=196 is approximately ( , )
?(Round to three decimal places as? needed.)
c. Choose the correct answer below.
A. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4.
B. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2.
C. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.