Suppose µ = 50 and ?² = 100 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

Question

Quizplus · Accepted Answer

This statement is consistent with the central limit theorem, which states that for large enough sample sizes, the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. A 95% confidence interval can be calculated by taking the sample mean plus or minus 1.96 times the standard error. Using the given values, we get:

Standard error = 100/sqrt(100) = 10
Lower bound = 50 - 1.96(10) = 48.04
Upper bound = 50 + 1.96(10) = 51.96

Therefore, 95% of all possible sample means will fall between 48.04 and 51.96.

Suppose µ = 50 and ?2 = 100 for a Population

Suppose µ = 50 and ?² = 100 for a Population