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 90 rainfalls are analyzed for pH, and x and s are equal to 3.9 and 0.8, respectively. Find a 99% confidence interval for the mean pH in rainfall. (Round your answers to three decimal places.)_______ to _______

Interpret the interval:

1)There is a 99% chance that an individual sample mean will fall within the interval.

2) In repeated sampling, 99% of all intervals constructed in this manner will enclose the population mean. 9

3) 9% of all values will fall within the interval.

4) There is a 1% chance that an individual sample mean will fall within the interval.

5) In repeated sampling, 1% of all intervals constructed in this manner will enclose the population mean.

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

1)The standard deviation must be less than 10.

2)The sample mean must be greater than 5.

3) The sample must be random.

4)There must be at least 100 samples.

5)The sampling distribution must be symmetrical.

Answer 1

Here n=90, as sample size is sufficient large so as per central limit theorem distribution of sample mean is normal.

Hence we will use z distribution to find CI

z value for 99% CI is 2.58 as

As s=0.8, margin of error is

So CI is

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

5. The sampling distribution must be symmetrical as for data to be normally distributed distribution needs to be symmetrical