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