Computing SEM and Constructing Confidence Levels
You can use this resource to learn more about computing the standard error of the mean (SEM) and using that value to construct a confidence interval. This handout will not delve into the conceptual pieces of this process, so if you’d like to learn more about the concepts, please use ASC Chat or Ask a Coach for additional assistance.
Computing SEM
To compute the standard error of the mean (SEM), you’ll need the standard deviation (σ) and the sample size (n). Here is a basic formula that you can use:
SEM = σ/√n
Example
You are studying IQ’s, which have a known mean and standard deviation of 100 and 15, respectively. For a randomly selected group of 49 students, what is the SEM?
SEM = σ/√n = 15/√49 = 15/7 = 2.14
Constructing Confidence Intervals
A confidence interval allows you to estimate the range of values that contains the true population mean for the selected sample. To construct this interval, you’ll need a point estimate of the population parameter (i.e. sample mean (x̄) to estimate population mean), a critical value (Z), and the SEM (σE). Here is a basic formula that you can use:
CI = x̄ ± Z(σE)
The value of Z will depend on the level of confidence given. Since Z is from a standardized distribution, this value does not change based on sample size. Here is a table of common values that you can use:
Confidence Level Critical Z
90% 1.645
95% 1.960
99% 2.576
Example
Let’s say your sample of 49 students had a mean IQ of 92. Construct the 95% confidence interval for the population mean.
95% CI = x̄ ± Z(σE) = 92 ± 1.960(2.14) = 92 ± 4.19
= 92 – 4.19 = 87.81
= 92 + 4.19 = 96.19
95% CI = (87.81, 96.19)
