Suppose that a 95% confidence interval states that population mean is greater than 100 and less than 300. Then the value of sample mean \((\bar{x})\) and margin of error (E) respectively are:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 200, ±100
A confidence interval for the population mean is centred at the sample mean, with the margin of error on each side:
\(\bar{x} - E = 100\)
\(\bar{x} + E = 300\)
Adding and subtracting the two equations:
\( \displaystyle \bar{x} = \frac{100 + 300}{2} = 200 \)
\( \displaystyle E = \frac{300 - 100}{2} = 100 \)
So the sample mean is 200 and the margin of error is ±100.