Here are summary statistics for randomly selected weights of newborn girls: \( \mathrm{n}=36, \overline{\mathrm{x}}=3197.2 \mathrm{~g}, \mathrm{~s}=692.6 \mathrm{~g} \). Use a confidence level of \( 90 \% \) to complete parts (a) through (d) below a. Identify the critical value \( \mathrm{t}_{\alpha / 2} \) used for finding the margin of error. \( \mathrm{t}_{\alpha / 2}=1.69 \) (Round to two decimal places as needed.) b. Find the margin of error. \( \mathrm{E}=195.0 \mathrm{~g} \) (Round to one decimal place as needed.) c. Find the confidence interval estimate of \( \mu \). \( \square \mathrm{g}<\mu<\square \mathrm{g} \) (Round to one decimal place as needed.)
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To find the confidence interval estimate of the population mean \( \mu \) based on the given statistics, we start by calculating the lower and upper limits of the confidence interval using the formula \( \overline{x} \pm E \). The sample mean \( \overline{x} = 3197.2 \, \text{g} \) and the margin of error \( E = 195.0 \, \text{g} \). Calculating the lower limit: - Lower limit = \( 3197.2 - 195.0 = 3002.2 \, \text{g} \). Calculating the upper limit: - Upper limit = \( 3197.2 + 195.0 = 3392.2 \, \text{g} \). Thus, the confidence interval estimate of \( \mu \) is: \( 3002.2 \, \text{g} < \mu < 3392.2 \, \text{g} \).