In this homework, you are required to construct the sampling distribution (of size n = 10) from a population (with population mean, µ=4.4 and standard deviation, σ=2.15). In order to simulate the sampling distribution of 𝑥̅, we have selected 50 samples (of size n = 10) with replacement from the population (with mean, µ=4.4 and standard deviation, σ=2.15), and have calculated the corresponding sample means. Sample means (for the 50 samples) are given as R dataset in the course webpage.
a.) Construct a relative frequency histogram for these 50 values of 𝑥̅. What is the shape of this distribution?
b.) Find the mean and standard deviation of the 50 values of 𝑥̅.
c.) Compare the values calculated in part a to the theoretical mean µ and the theoretical standard deviation 𝜎⁄ for the sampling distribution of 𝑥̅. How close do the values calculated from the 50 measurements come to the theoretical values?
