Q Save \& Exit Certify Lesson: 8.3 Estimating Population Means (... Question 2 of 10, Step 1 of 2 In a random sample of 7 residents of the state of Montana, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.16 pounds. Determine the \( 90 \% \) confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

To find the critical value for constructing a 90% confidence interval, you would typically use a t-distribution, especially since your sample size is small (n = 7). For a 90% confidence level and 6 degrees of freedom (n-1 = 7-1), you can look up the critical value in the t-table or use a calculator. The critical t-value is approximately 1.943. This means that you can now calculate your confidence interval using this t-value along with your sample mean and standard deviation. Remember, the formula for the confidence interval is: \[ \text{CI} = \bar{x} \pm (t \times \frac{s}{\sqrt{n}}) \] Where \(\bar{x}\) is the sample mean, \(t\) is the critical value, \(s\) is the standard deviation, and \(n\) is the sample size. Enjoy digging into those numbers!