In this homework, you are required to construct the sampling distribution (of size n = 10) from a population (with population mean, Β΅=4.4 and standard deviation, Ο=2.15).Β In order to simulate the sampling distribution of π₯Μ , we have selected 50 samples (of size n = 10) with replacement from the population (with mean, Β΅=4.4 and standard deviation, Ο=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 π₯Μ . What is the shape of this distribution?
- Find the mean and standard deviation of the 50 values of π₯Μ .
- Compare the values calculated in part a to the theoretical mean Β΅ and the theoretical standard deviation πβ for the sampling distribution of π₯Μ . How close do the values calculated from the 50 measurements come to the theoretical values?
Deliveries:Β
- 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.
