Questions: When σ is unknown, the margin of error is computed by using

Solution Steps

For a confidence level of \( 95\% \), the Z-score is given by:

\[ Z = 1.96 \]

The formula for the margin of error \( E \) when the population standard deviation is unknown is:

\[ E = \frac{Z \times s}{\sqrt{n}} \]

where:

• \( s = 10.0 \) (sample standard deviation)
• \( n = 30 \) (sample size)

Substituting the values into the formula:

\[ E = \frac{1.96 \times 10.0}{\sqrt{30}} \]

Calculating the margin of error:

\[ E = \frac{19.6}{\sqrt{30}} \approx \frac{19.6}{5.4772} \approx 3.5784 \]

Final Answer