Question

Write a function in R that will provide the sample size needed (using the confidence interval method) to estimate the true population mean. You will have to pass several input variables to this function: confidence level, margin of error, and estimated standard deviation.

Answer 1

To calculate the sample size we have the formula;

n = (z_α∕2²*σ²)/(e²)

Here n = Sample Size
z_α∕2 is the 100(1 − α∕2) percentile of the standard normal distribution
e = margin of error
σ²= standard deviation

#Let us assume we have to calculate at a conf interval of 95%, standard deviation =10, margin of error = 1.5

z = qnorm(.975) #Since there are two tails of the normal distribution, the 95% confidence level would imply the 97.5th percentile of the normal distribution at the upper tail.
sigma = 10 # Value of sd given
e = 1.5 # margin of error

n <- z^2 ∗ sigma^2/ e^2 #n is the sample size

print(n) # Printing the value of n

#Output
[1] 170.7315

Based on the assumption of population standard deviation being 10, it needs a sample size of 171 to achieve a 1.5 margin of error at 95% confidence level.

However we know that the quality of a sample survey can be improved by increasing the sample size.