North South UniversitySchool of Life Sciences

Sampling Variability, Confidence Intervals, and p-values for Means and Differences in MeansObaidur 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 amean 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?

sample size greater than 30

Solution

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