Question

Your power plant emits nitrous oxides (NOx) into the atmosphere as a byproduct of burning coal. While your scrubbers collect much of the pollutant before it leaves your smokestacks, they cannot get it all. You have an allowance of one hundred pounds of NOx per day. The state environmental commission shows up periodically to test whether you are staying within your allowance. If you are not within your allowance, you will have to purchase more allowance from a plant that is not using all of theirs (a costly proposition). You periodically test your smoke to see how things are going. The numbers in the table represent a test of n = 10 randomly selected days over the past month.

a. Construct a 95% confidence interval for your average daily pounds of pollutants.

b. Should you be worried? Why, why not?  

Day	Pounds
1	99
2	85
3	82
4	102
5	90
6	110
7	108
8	91
9	93
10	106

Answer 1

Solution: a. Construct a 95% confidence interval for your average daily pounds of pollutants.

Answer: The 95% confidence interval for the average daily pounds of pollutants is:

Where:

is the sample mean

is the sample standard deviation

is the sample size

is the critical value at 0.05 significance level for and is given:

We need to first find the sample mean and sample standard deviation of the pounds data:

Therefore, the 95% confidence interval is:

Therefore, the 95% confidence interval for the average daily pounds of pollutants is:

b. Should you be worried? Why, why not?

Answer: We should be worried, because the upper limit of the 95% confidence interval is further away from the maximum allowance of one hundred pounds of NOx per day.