Question 1 of 7. Step 2 of 2 $1 / 12$ Correct 3 In a random sample of 13 residents of the state of Washington, the mean waste recycled per person per day was 1.6 pounds with a standard deviation of 0.43 pounds. Determine the $98 \%$ confidence interval for the mean waste recycled per person per day for the population of Washington. Assume the population is approximately normat: Step 2 of 2 : Construct the $98 \%$ confidence interval. Round your answer to one decimal place. Answer How to enter your answer (opens in new window) Tables Keypad Keyboard Shortcuts
Solution
Step 1 ：Given values are mean = 1.6, standard deviation = 0.43, sample size = 13, and Z-score for 98% confidence interval = 2.33.
Step 2 ：Calculate the margin of error using the formula: \(Z \times \frac{standard deviation}{\sqrt{sample size}}\).
Step 3 ：Substitute the given values into the formula to get the margin of error = 0.27787706329902856.
Step 4 ：Calculate the lower bound of the confidence interval using the formula: \(mean - margin of error\). Substitute the given values into the formula to get the lower bound = 1.3.
Step 5 ：Calculate the upper bound of the confidence interval using the formula: \(mean + margin of error\). Substitute the given values into the formula to get the upper bound = 1.9.
Step 6 ：The 98% confidence interval for the mean waste recycled per person per day for the population of Washington is \(\boxed{(1.3, 1.9)}\) pounds.
