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- This handout will assist you with computing the standard error of the mean (SEM) and using that value to construct a confidence interval.

**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 (σ_{E}). Here is a basic formula that you can use:

CI = x̄ ± Z(σ_{E})

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(σ_{E}) = 92 ± 1.960(2.14) = 92 ± 4.19

= 92 – 4.19 = 87.81

= 92 + 4.19 = 96.19

95% CI = (87.81, 96.19)

- Last Updated: Mar 12, 2023 6:02 PM
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