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