Save \& Exit Certify 11/19 Question 7 of 10 , Step 2 of 2 3 In a random sample of 11 residents of the state of Florida, the mean waste recycled per person per day was 2.9 pounds with a standard deviation of 0.42 pounds. Determine the \( 95 \% \) confidence interval for the mean waste recycled per person per day for the population of Florida. Assume the population is approximately normal. Step 2 of 2 : Construct the \( 95 \% \) confidence interval. Round your answer to one decimal place. Tables Keypad

To construct a \( 95\% \) confidence interval for the mean waste recycled per person per day, you can use the formula: \[ CI = \bar{x} \pm t^\ast \left(\frac{s}{\sqrt{n}}\right) \] Where: - \( \bar{x} = 2.9 \) pounds (sample mean) - \( s = 0.42 \) pounds (sample standard deviation) - \( n = 11 \) (sample size) First, find the critical value \( t^\ast \) for \( n-1 = 10 \) degrees of freedom at a \( 95\% \) confidence level. This is approximately \( 2.228 \). Now calculate the standard error (SE): \[ SE = \frac{s}{\sqrt{n}} = \frac{0.42}{\sqrt{11}} \approx 0.1261 \] Now, calculate the margin of error (ME): \[ ME = t^\ast \times SE = 2.228 \times 0.1261 \approx 0.280 \] Finally, construct the confidence interval: \[ CI = 2.9 \pm 0.280 \implies (2.6, 3.2) \] Thus, the \( 95\% \) confidence interval for the mean waste recycled per person per day in Florida is approximately \( (2.6, 3.2) \) pounds.