Question 1
Express the confidence interval $34.7 \% \pm 4.8 \%$ in interval form.
Express the answer in decimal format (do not enter as percents).
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Answer
The confidence interval in interval form is \(\boxed{(0.299, 0.395)}\).
Step 1 ：Convert the given percentages to decimals by dividing by 100. So, \(34.7 \% = \frac{34.7}{100} = 0.347\) and \(4.8 \% = \frac{4.8}{100} = 0.048\).
Step 2 ：Subtract the decimal equivalent of the percentage from the mean to get the lower limit of the interval. So, \(0.347 - 0.048 = 0.299\).
Step 3 ：Add the decimal equivalent of the percentage to the mean to get the upper limit of the interval. So, \(0.347 + 0.048 = 0.395\).
Step 4 ：The confidence interval in interval form is \(\boxed{(0.299, 0.395)}\).
