Question 16 1 pts Kingsnorth et al. (2002) examined the case processing time (in days) from arraignment to disposition for cases processed by the Sacramento County District Attorney's office. For the 58 cases that were rejected at intake, the mean processing time was 11.3 days with a standard deviation of 21.02 . Construct $95 \%$ confidence intervals for the mean. What is the UPPER bound for the confidence interval? 17.65 15.23 16.71 16.02
Solution
Step 1 ：We are given that the mean processing time is \(\bar{x} = 11.3\) days, the standard deviation is \(s = 21.02\) days, the sample size is \(n = 58\), and the z-score for a 95% confidence level is \(z = 1.96\).
Step 2 ：We are asked to find the upper bound of the 95% confidence interval for the mean. The formula for the confidence interval of the mean is \(\bar{x} \pm z \frac{s}{\sqrt{n}}\).
Step 3 ：To find the upper bound, we use the formula \(\bar{x} + z \frac{s}{\sqrt{n}}\).
Step 4 ：Substituting the given values into the formula, we get \(11.3 + 1.96 \frac{21.02}{\sqrt{58}}\).
Step 5 ：Solving the above expression, we get the upper bound as approximately 16.71.
Step 6 ：Final Answer: The UPPER bound for the confidence interval is \(\boxed{16.71}\).
