Question

you randomly select and measure the contents of 10 bottles of cough syrup. the results (in fluid ounces) are shown to the right. 4.218 4.298 4.253 4.242 4.188 4.244 4.265 4.246 4.221 4.236 assume the sample is taken from a normally distributed population. construct 80% confidence intervals for (a) the population variance σ² and (b) the population standard deviation σ. interpret the results. (a) the confidence interval for the population variance is (0.000530, 0.001860). (round to six decimal places as needed.) interpret the results. select the correct choice below and fill in the answer box(es) to complete your choice. (round to six decimal place as needed.) a. with 20% confidence, it can be said that the population variance is between and. b. with 80% confidence, it can be said that the population variance is greater than. c. with 80% confidence, it can be said that the population variance is between 0.000530 and 0.001860. d. with 20% confidence, it can be said that the population variance is less than. (b) the confidence interval for the population standard deviation is (□,□). (round to four decimal places as needed.)

Explanation:

Step1: Recall the relationship between variance and standard deviation

The standard deviation \(\sigma\) is the square - root of the variance \(\sigma^{2}\). If the confidence interval for the variance is \((a,b)\), then the confidence interval for the standard deviation is \((\sqrt{a},\sqrt{b})\)

Step2: Calculate the square - roots

Given \(a = 0.000530\) and \(b=0.001860\)
For the lower bound: \(\sqrt{0.000530}\approx0.0230\)
For the upper bound: \(\sqrt{0.001860}\approx0.0431\)

Answer:

\((0.0230,0.0431)\)