The data shown below represent the repair cost for a low-impact collision in a simple random sample of mini- and micro-vehicles (such as the Chevrolet Aveo or Mini Cooper). Complete parts (a) through (c). \[ \begin{array}{l} \$ 3130 \quad \$ 1084 \quad \$ 721 \quad \$ 661 \quad \$ 793 \text { 문 } \\ \$ 1755 \$ 3328 \$ 2007 \$ 2605 \$ 1350 \\ \end{array} \] Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. Click here to view the table of critical t-values. If the boxplot suggests a confidence interval can be constructed, calculate and interpret the lower bound and the upper bound of the confidence interval. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round to the nearest dollar. Use ascending order.) A. There is a $95 \%$ probability that the mean cost of repair is between $\$$ and $\$ \square$. B. We are $95 \%$ confident that the mean cost of repair is between $\$$ and $\$ \square$. c. The confidence interval should not be constructed.
Solution
Step 1 ：Given the repair costs for a low-impact collision in a simple random sample of mini- and micro-vehicles, we have the following data: \$3130, \$1084, \$721, \$661, \$793, \$1755, \$3328, \$2007, \$2605, \$1350.
Step 2 ：First, we calculate the mean of the data, which is \$1743.4.
Step 3 ：Next, we calculate the standard deviation of the data, which is \$997.51.
Step 4 ：The sample size, denoted as \(n\), is 10.
Step 5 ：We then calculate the t-score for a 95% confidence interval, which is 2.262.
Step 6 ：Using these values, we can calculate the lower and upper bounds of the confidence interval. The lower bound is calculated as \(mean - t\_score \times \frac{std\_dev}{\sqrt{n}}\), which gives us \$1029.82. The upper bound is calculated as \(mean + t\_score \times \frac{std\_dev}{\sqrt{n}}\), which gives us \$2456.98.
Step 7 ：Rounding to the nearest dollar, we get the lower bound as \$1030 and the upper bound as \$2457.
Step 8 ：\(\boxed{\text{Final Answer: We are 95% confident that the mean cost of repair is between \$1030 and \$2457.}}\)
