A simple random sample of 50 items from a population with \( \sigma=6 \) resulted in a sample mean of 32. If the margin of error is 1.66, then the 95% confidence interval for the population mean is:
[Given : \( Z_{0.025}=1.96 \)]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (30.34, 33.66)
The confidence interval is the sample mean plus or minus the margin of error:
\( \displaystyle \overline{x}\pm E=32\pm 1.66 \)
\( \displaystyle =(30.34,\ 33.66) \)
The given margin agrees with \( 1.96\cdot\frac{6}{\sqrt{50}}\approx 1.66 \).