Solution Found!
From the data on CAT scans in Exercise 8-45(a) Find a
Chapter 8, Problem 58E(choose chapter or problem)
From the data on CAT scans in Exercise 8-45
(a) Find a two-sided 95% confidence interval for the standard deviation.
(b) What should you do to address any reservations about the confidence interval you found in part (a)?
Questions & Answers
QUESTION:
From the data on CAT scans in Exercise 8-45
(a) Find a two-sided 95% confidence interval for the standard deviation.
(b) What should you do to address any reservations about the confidence interval you found in part (a)?
ANSWER:Step 1 of 4
Given,
The sample size, \(n=12\)
The confidence interval, \(\mathrm{Cl}=95 \%\)
Let’s calculate the mean of the CAT scans,
\(\begin{aligned} \bar{x} & =\frac{2.31+2.09+\cdots+2.02}{12} \\ \bar{x} & =\frac{24.98}{12} \\ \bar{x} & =2.0817 \end{aligned}\)
Now, let’s calculate the standard deviation,
\(\begin{array}{l} s=\sqrt{\frac{(2.31-2.0817)^{2}+(2.09-2.0817)^{2}+\cdots+(2.02-2.0817)^{2}}{12-1}} \\ s=\sqrt{\frac{0.269}{11}} \\ s=0.15637 \end{array}\)