Question

as part of a water quality survey, you test the water hardness in several randomly selected streams. the results are shown below. construct a confidence interval for the population variance \\( \sigma^{2} \\) and the population standard deviation \\( \sigma \\). use a 99% level of confidence. assume that the population has a normal distribution.
\\( n = 24 \\)
\\( s = 14 \\) grains per gallon
what is the confidence interval for the population standard deviation \\( \sigma \\)?
\\( (10.1,22.1) \\) (round to one decimal place as needed.)
interpret the results. select the correct choice below and fill in the answer box(es) to complete your choice.
(round to one decimal places as needed.)
\\( \bigcirc \\) a. with 1% confidence, you can say that the
\\( \bigcirc \\) b. with 99% confidence, you can say that the
population standard deviation is greater than
population standard deviation is between \\( \square \\) and
\\( \square \\) grains per gallon.
\\( \square \\) grains per gallon.
\\( \bigcirc \\) c. with 99% confidence, you can say that the
\\( \bigcirc \\) d. with 1% confidence, you can say that the
population standard deviation is less than \\( \square \\)
population standard deviation is between \\( \square \\) and
\\( \square \\) grains per gallon.
\\( \square \\) grains per gallon.

Explanation:

A confidence interval gives a range of values within which the population parameter (here, the standard deviation) is likely to lie. A 99% confidence level means that if we were to construct many such intervals from different samples, 99% of them would contain the true population standard deviation. Since the calculated confidence interval for the population standard deviation is (10.1, 22.1), we interpret it based on the confidence level used in construction.

Answer:

B. With 99% confidence, you can say that the population standard deviation is between 10.1 and 22.1 grains per gallon.