Question

the diameters (in inches) of 17 randomly selected bolts produced by a machine are listed. use a 90% level of confidence to construct a confidence interval for (a) the population variance $\sigma^{2}$ and (b) the population standard deviation $\sigma$. interpret the results.
4.472 4.424 4.027 4.311 4.007 3.789
3.816 3.771 4.239 3.957 4.148 4.528
3.935 3.763 3.883 3.809 4.449
(b) the confidence interval for the population standard deviation is (0.214, 0.389).
(round to three decimal places is needed.)
interpret the results. select the correct choice below and fill in the answer box(es) to complete your choice.
(round to three decimal place as needed.)
○ a. with 10% confidence, you can say that the population standard deviation is between and inches.
○ b. with 90% confidence, you can say that the population standard deviation is between and inches.
○ c. with 10% confidence, you can say that the population standard deviation is greater than inches.
○ d. with 90% confidence, you can say that the population standard deviation is less than inches.

Explanation:

A confidence interval is a range of values within which we are confident the true population parameter lies. A 90% confidence level means that if we were to construct many such intervals from different samples, approximately 90% of them would contain the true population parameter. In this case, the confidence interval for the population standard deviation ($\sigma$) is given as (0.214, 0.389). This interval is constructed based on the sample data and the properties of the chi - square distribution (since we are dealing with variance and standard deviation confidence intervals).

Answer:

B. With 90% confidence, you can say that the population standard deviation is between 0.214 and 0.389 inches.