 # Sampling Variability, Confidence Intervals, and p

```North South University
School of Life Sciences
Sampling Variability, Confidence Intervals,
and p-values for Means and Differences in
Means
Obaidur Rahman, PhD.
NSU
Section A
The Random Sampling Behavior of a Sample
Mean Across Multiple Random Samples
Section B
The Theoretical Sampling Distribution of the Sample Mean
and Its Estimate Based on a Single Sample
Section C
Estimating Confidence Intervals for the Mean of a
Population Based on a Single Sample of Size n: Some
Examples
NSU
NSU
NSU
Section C
Practice Problems
Section D
True Confessions Biostats Style: What We Mean by
Approximately Normal and What Happens to the Sampling
Distribution of the Sample Mean with Small n
Section D
Practice Problems
Problem
Suppose it is known that in a certain large human population
cranial length is approximately normally distributed with a
mean of 185.6 mm and a standard deviation of 12.7
mm.
What is the probability that a random sample of size 10 from
this population will have a mean greater than 190?
Solution
By consulting the standard normal table,
we ﬁnd that the area to the right of 1.10
is .1357; hence, we say that the probability is
.1357 that a sample of size 10 will have a
mean greater than 190.
Problem
If the mean and standard deviation of serum iron values for healthy men
are 120 and 15 micrograms per 100 ml, respectively, what is the
probability that a random sample of 50 normal men will yield a mean
between 115 and 125 micrograms per 100 ml?
Solution
sample size greater than 30
Problem
Solution
Problem
Solution
Problem
Solution
Section E
The Sample Proportion as a Summary Measure for Binary
Outcomes and the CLT
Section F
The Theoretical Sampling Distribution of the Sample
Proportion and Its Estimate Based on a Single Sample
Section F
Practice Problems
Section G
Estimating Confidence Intervals for the Proportion of a
Population Based on a Single Sample of Size n: Some
Examples
Section G
Practice Problems
Section H
Small Sample Considerations for Confidence
Intervals for Population Proportions
The End
``` # Small-Sample C.I.s for one- sample, two-sample and (matched) paired data # Sampling Theory and Applications www.american.edu/sampta2015 # PROTEqIN Survey â Description and Methodological Brief 