- Question 1 You measure 39 dogs' weights, and find they have a mean weight of 41 ounces. Assume the population standard deviation is 8.7 ounces. Based on this, construct a $90 \%$ confidence interval for the true population mean dog weight. Give your answers as decimals, to two places \[ \pm \] ounces Calculator Next Question

Step 1 ：Given values are: sample mean (\(x_{bar}\)) = 41, Z-score (Z) = 1.645, population standard deviation (\(\sigma\)) = 8.7, and sample size (n) = 39.

Step 2 ：Calculate the margin of error using the formula: Margin of Error = Z * (\(\sigma\) / \(\sqrt{n}\)).

Step 3 ：Substitute the given values into the formula: Margin of Error = 1.645 * (8.7 / \(\sqrt{39}\)) = 2.29 (rounded to two decimal places).

Step 4 ：Calculate the confidence interval using the formula: Confidence Interval = \(x_{bar}\) ± Margin of Error.

Step 5 ：Substitute the values into the formula: Lower Limit = 41 - 2.29 = 38.71 and Upper Limit = 41 + 2.29 = 43.29.

Step 6 ：Final Answer: The 90% confidence interval for the true population mean dog weight is approximately \(\boxed{38.71}\) ounces to \(\boxed{43.29}\) ounces.