Question

A sample of size n=11 is drawn from an approximately normal population whose standard deviation is σ=9.5. The sample mean is x=44.9 Construct a 90% confidence interval for μ.

Answer 1

To construct a 90% confidence interval for μ, calculate the margin of error using the formula EBM = Z * (σ/√n), where Z is the Z-value for the desired confidence level.

Step-by-step explanation:

To construct a 90% confidence interval for the population mean, we need to calculate the margin of error and then find the lower and upper bounds of the interval.

First, we calculate the margin of error using the formula:
Margin of Error (EBM) = Z * (σ/√n)

Since the sample size (n) is 11 and the standard deviation (σ) is 9.5, we can use a Z-value of 1.645 for a 90% confidence level (looked up from a t-table or Z-table).

Substituting the values into the formula, we can find the margin of error:
EBM = 1.645 * (9.5/√11) ≈ 5.269

To find the lower and upper bounds of the confidence interval, we subtract and add the margin of error from the sample mean:
Lower Bound = x - EBM = 44.9 - 5.269 ≈ 39.631
Upper Bound = x + EBM = 44.9 + 5.269 ≈ 50.169

The 90% confidence interval for μ is approximately (39.631, 50.169).