Solution:Bootstrapping technique is used to obtain the sampling distribution of parameters of interest.
Goal: Estimate the sampling distribution of the sample mean using bootstrapped.
Step 1: Start with observed data (the sample) suppose we have this small dataset of incomes (in $ 1000s):
Data = [45, 50, 55, 60, 65)
Sample sizes (n) = 5
Step-2 Bootstrap Reasmplilng
Resample with replacement from the original data-say,
5 values each time (same size as the original)
: Resample 1 (50,60,60,45,55)- Mean= 54
: Resample 2 (65,65,55,50,65)- Mean= 60
: Resample 3 (45,45,55,50,45)- Mean= 48
Do theis B= 1000 times to get 1000 bootstrap sample means.
Step 3: Build the sample Distribution
now, you have 1000 bootstrapped mean, for eg. Boots trap means = (54,60,48.......57)
This set forms a empirical approximation of the sampling distributioin of the sample mean
Step 4: Use the sampling Distribution
• Estimate standard error of the mean.
• Construct confidence intervals.
• Do hypothesis testing