A simple random sample of 49 items from a population with standard deviation, σ = 6 resulted in a sample mean of 32. At 95% confidence level, the margin of error is (Given \( Z_{0.025}=1.96 \))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1.68
When the population standard deviation is known, the margin of error is
\( \displaystyle E=Z_{0.025}\times\frac{\sigma}{\sqrt{n}} \)
\( \displaystyle =1.96\times\frac{6}{\sqrt{49}} \)
\( \displaystyle =1.96\times\frac{6}{7} \)
\( \displaystyle =1.68 \)
The sample mean 32 is not needed for the margin of error.