Question

nal examination
nal examination
0 points possible answered: 8/12
question 9
express the confidence interval 78% ± 8.5% in interval form.
express the answer in decimal format (do not enter as percents).

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Explanation:

Step1: Convert percentages to decimals

First, convert \(78\%\) to decimal: \(78\%=\frac{78}{100} = 0.78\). Then, convert \(8.5\%\) to decimal: \(8.5\%=\frac{8.5}{100}=0.085\).

Step2: Find the lower and upper bounds

The confidence interval is given as \( \text{estimate} \pm \text{margin of error} \). So the lower bound is \(0.78 - 0.085\) and the upper bound is \(0.78+ 0.085\).

Calculate the lower bound: \(0.78 - 0.085=0.695\).

Calculate the upper bound: \(0.78 + 0.085 = 0.865\).

Step3: Write in interval form

The interval form of a confidence interval \(\hat{p}\pm E\) is \((\text{lower bound}, \text{upper bound})\), so here it is \((0.695, 0.865)\).

Answer:

\((0.695, 0.865)\)