A simple random sample of 49 items from a population with standard deviation 10 resulted in a sample mean of 25. Then the 95% confidence interval for population mean are :
(Given \( z_{\alpha/2}=1.96 \) where \( \alpha=0.05 \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (22.2, 27.8)
With the population standard deviation σ known, the confidence interval for the population mean is
\( \displaystyle \bar{x}\pm z_{\alpha/2}\,\frac{\sigma}{\sqrt{n}} \)
\( \displaystyle \bar{x}=25,\ \sigma=10,\ n=49 \)
\( \displaystyle \frac{\sigma}{\sqrt{n}}=\frac{10}{7} \)
\( \displaystyle 1.96\times\frac{10}{7}=2.8 \)
\( \displaystyle 25-2.8=22.2 \)
\( \displaystyle 25+2.8=27.8 \)
So the 95% confidence interval is (22.2, 27.8).