Acid rain, caused by the reaction of certain air pollutants with rainwater, is a

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 3.5 and 0.9, respectively. Find a 99% confidence interval for the mean pH in rainfall. (Round your answers to three decimal places.)
_ to _

Interpret the interval.

There is a 1% chance that an individual sample mean will fall within the interval.99% of all values will fall within the interval.    In repeated sampling, 1% of all intervals constructed in this manner will enclose the population mean.There is a 99% chance that an individual sample mean will fall within the interval.In repeated sampling, 99% of all intervals constructed in this manner will enclose the population mean.

What assumption must be made for the confidence interval to be valid?

The sample must be random.The sample mean must be greater than 5.    The standard deviation must be less than 10.The sampling distribution must be symmetrical.There must be at least 100 samples.

Explanation / Answer

Ans:

Given that

sample mean=3.5

s=0.9

n=40

df=40-1=39

critical t value=tinv(0.01,39)=2.708

99% confidence interval for population mean

=3.5+/-2.708*(0.9/sqrt(40))

=3.5+/-0.385

=(3.115, 3.885)

In repeated sampling, 99% of all intervals constructed in this manner will enclose the population mean.

The sample must be random.

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