Question 17
1 pts

Let's say you have a sample of 10 young males who have committed serious offences over the course of their lives. The average age at first arrest is 12, with a standard deviation of 2.3. Construct a $95 \%$ confidence interval around the mean.

What is your UPPER bound?
13.05
12.50
12.36
13.66

Step 1 ：The formula for constructing a 95% confidence interval for the mean is: \(\text{Mean} \pm (t\text{-value} \times \frac{\text{standard deviation}}{\sqrt{\text{sample size}}})\)

Step 2 ：The t-value for a 95% confidence interval with 9 degrees of freedom (10 - 1) is approximately 2.262 (from the t-distribution table).

Step 3 ：Substitute the given values into the formula: \(12 \pm (2.262 \times \frac{2.3}{\sqrt{10}})\)

Step 4 ：Calculate the value inside the parentheses: \(2.262 \times \frac{2.3}{\sqrt{10}} = 1.62\) (rounded to two decimal places)

Step 5 ：Add this value to the mean to get the upper bound: \(12 + 1.62 = 13.62\)

Step 6 ：\(\boxed{13.62}\) is the upper bound of the 95% confidence interval.