Description
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.
- Construct a relative frequency histogram for these 50 values of 𝑥̅. What is the shape of this distribution?
- Find the mean and standard deviation of the 50 values of 𝑥̅.
- 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?
Deliveries:
- The R code you developed (RStudio). For each question, you need to plot the data according to your needs.
- A report that includes the answers to the questions above.
