9.4 Full hypothesis test examples

Given a random variable (RV) with known mean μ and known standard deviation σ. We are sampling with size n and we are interested in two new RVs - the sample mean, X ¯ . If the size n of the sample is sufficiently large, then X ¯ ~ N ( μ , σ n ) . If the size n of the sample is sufficiently large, then the distribution of the sample means will approximate a normal distribution regardless of the shape of the population. The expected value of the mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, σ n , is called the standard error of the mean.