Suppose ? = 80 and $\sigma$= 20 for a population.In a sample where n = 100 is randomly taken,95% of all possible sample means will fall above 76.08.

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Quizplus · Accepted Answer

This is true because the sample mean is an unbiased estimator of the population mean and the standard error of the mean (SE) is equal to the population standard deviation (σ) divided by the square root of the sample size (n). Using the formula for the SE, SE = σ/√n = 20/√100 = 2. Therefore, a 95% confidence interval for the population mean would be 80 ± 1.96(2) or (75.16, 84.84). Since 76.08 > 75.16, it is true that 95% of all possible sample means will fall above 76.08.

Suppose ? = 80 And σ\sigmaσ = 20 for a Population

Suppose ? = 80 And $\sigma$ = 20 for a Population