A simple random sample of 64 items from a population with standard deviation \( \sigma=4 \) resulted in a sample mean of 35. What is the margin of error for the population mean at a 95% confidence level? (Given Z0.025 = 1.96)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.98
With the population standard deviation known, the margin of error at 95% confidence is
\( \displaystyle E=z_{0.025}\times\frac{\sigma}{\sqrt{n}} \)
\( \displaystyle =1.96\times\frac{4}{\sqrt{64}} \)
\( \displaystyle =1.96\times\frac{4}{8} \)
\( \displaystyle =1.96\times 0.5=0.98 \)
Tip: The sample mean 35 is not needed for the margin of error; it is used only to write the confidence interval \( 35\pm 0.98 \).