Questions: A sample of size n=38 is drawn from a population whose standard deviation is σ=44. Find the margin of error for a 90% confidence interval for μ. Round the answer to at least three decimal places. The margin of error for a 90% confidence interval for μ is

Solution Steps

For a 90% confidence interval, the Z-score corresponding to the critical value is:

\[ Z = 1.645 \]

The formula for the margin of error \(E\) is given by:

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

Substituting the known values:

• \(Z = 1.645\)
• \(\sigma = 44\)
• \(n = 38\)

We can compute the margin of error as follows:

\[ E = \frac{1.645 \times 44}{\sqrt{38}} \]

Calculating the denominator:

\[ \sqrt{38} \approx 6.164 \]

Now substituting back into the equation:

\[ E = \frac{1.645 \times 44}{6.164} \approx \frac{72.38}{6.164} \approx 11.741 \]

Final Answer