Suppose μ = 50 and σ² = 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.

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Quizplus · Accepted Answer

This is a true statement based on the central limit theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution with mean μ and standard deviation σ/√n. Using this formula, we can calculate that the standard error of the mean for a sample size of 100 is σ/√n = 10. Therefore, a 95% confidence interval for the sample mean would be μ ± 1.96(10), which is 50 ± 19.6. This gives us the range of 48.04 to 51.96, which encompasses 95% of all possible sample means.

Suppose μ = 50 and σ2 = 100 for a Population

Suppose μ = 50 and σ² = 100 for a Population