We draw a random sample of size 36 from a population with the standard deviation 3.5.If the sample mean is 27,what is a 95% confidence interval for the population mean?
A)[25.8567,28.1433]
B)[26.0405,27.9595]
C)[26.8100,27.1900]
D)[26.8401,27.1599]

Question

Quizplus · Accepted Answer

The correct answer is A.The formula for a 95% confidence interval for the population mean is:sample mean +/- 1.96 * (standard deviation / square root of sample size)Plugging in the given values, we get:27 +/- 1.96 * (3.5 / square root of 36)= 27 +/- 1.96 * (3.5 / 6)= 27 +/- 1.96 * 0.583= 27 +/- 1.143= [25.8567, 28.1433]

We Draw a Random Sample of Size 36 from a Population