R Notebook

SI | Practical 1

R Practical to demonstrate Sampling Distribution

Theory

A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population.

A population may refer to an entire group of people, objects, events, hospital visits, or measurements.

Syntax

1. hist(v, main, xlab, ylab, col)

where:

• v is the vector containing values in the histogram

• main indicates the title of the chart

• col is used to set the colors of the bars

• xlab, ylab give the description of the x axis and y axis respectively

2. The rep() function is used to replicate values, and returns a vector

rep(x, times, each, length.out)

where:

• x is the vector to be replicated

• times is the number of times to repeat the entire vector

• each is the number of times to repeat each element of the vector

• length.out is the desired length of the output vector (extends or truncates the result)

Step 1: Define the vector of sample_means

n <- 1000

# create an empty vector of length n with null (NA) values using `rep()` function

sample_means <- rep(NA, n)

# fill empty vector with the sample means using `rnorm()` function with given mean and s.d. 

for (i in 1:n) {
  sample_means[i] <- mean(rnorm(20,
                                mean=10),
                          sd=10)
}

# return first 6 rows
head(sample_means)

[1] 10.455941  9.989466 10.387226 10.426577 10.088227
[6] 10.293503

Step 2: Create a histogram to visualize

hist(sample_means,
     main="Sampling Distribution",
     xlab="Sample Means",
     ylab="Frequency",
     col='blue')

Step 4: To cross check, find the mean and s.d.

mean(sample_means)

[1] 10.01324

sd(sample_means)

[1] 0.2261214

Step 5: To find the probability of a generated sample mean having mean >= 10

sum(sample_means >= 10) / length(sample_means)

[1] 0.514