Question

What two things happen to your sampling distribution as you increase sample size? . Suppose you have a normally distributed population. You decide to collect 10 samples from this population and your colleague collects 30 samples from this population. a. Hand draw the original population, your sampling distribution, and your colleague’s sampling distribution. b. What changes as you increase the sample size?

Answer 1

Sol:

n1=10,n2=30

sample follow normal distribution

sampling distribution follows normal distribution as original population follows normal distribution

Solutionb:

as we increase sample size standard error decreases

For ex

sigma=100

for n=10

standard error=100/sqrt(10)= 31.62278

sigma=100

for n=30

standard error=100/sqrt(30)= 18.25742

standard error decreases from 31.62278 to 18.25742 when sample size increased from 10 to 30

Also when we increase sample size,width of the interval decreases for any given confidence coefficient

For say 95% confidence interval

sigma=100

xbar=50

MARGIN OF ERROR WHEN n=10

=CONFIDENCE.NORM(0.05,100,10)

=61.9795

lower limit=xbar-moe=50-61.9795= -11.9795

upper limit=xbar+moe=50+61.9795=111.9795

MARGIN OF ERROR WHEN n=30

=CONFIDENCE.NORM(0.05,100,30)

=35.78388287

lower limit=xbar-moe=50-35.78388287=  14.21612

upper limit=xbar+moe=50+35.78388287= 85.78388

so width of the interval decreased when we increased sample size from 10 to 30

as we increase sample size standard error decreases

width of the interval decrease when we increased sample size