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Publication date: 04/21/2023

Margin of Error for One Sample Mean

Use the Margin of Error for One Sample Mean Explorer to determine a sample size for a confidence, prediction, or tolerance interval for one sample mean. Select DOE > Sample Size Explorers > Confidence Intervals > Margin of Error for One Sample Mean. Explore the trade offs between variability assumptions, sample size, significance, and the margin of error.

Interval Explorer for One Sample Mean Settings

Set study assumptions and explore sample sizes using the radio buttons, text boxes, and menus. The profiler updates as you make changes to the settings. Alternatively, change settings by dragging the cross hairs on the profiler curves.

Interval Type

One-sided

Specifies a one-sided interval (upper or lower bound)

Two-sided

Specifies a two-sided interval.

Interval Purpose

Confidence

Specifies a confidence interval for a mean.

Prediction

Specifies a prediction interval for one future observation.

Tolerance

Specifies a tolerance interval to cover a proportion of the population.

Preliminary Information

Alpha

Specifies the confidence level is 1 - alpha. The default alpha level is 0.05 for a 95% confidence interval.

Proportion

(Available only when Tolerance is selected for Interval Purpose.) Specifies the proportion of the population for the tolerance interval to cover.

Population Standard Deviation

Specifies the distribution for calculations.

Yes

Specifies a known standard deviation, calculations use the z distribution.

No

Specifies an unknown standard deviation, calculations use the t distribution.

Interval Explorer for One Sample Mean Profiler

The profiler enables you to visualize the impact of sample size assumptions on the margin of error calculations.

Solve for

Enables you to solve for the sample size or assumed standard deviation.

Margin of Error

Specifies the half-width of the interval. With all other parameters fixed, margin of error decreases as sample size increases.

Sample Size

Specifies the total number of observations (runs, experimental units, or samples) needed to construct your interval.

Std Dev (σ)

Specifies the assumed population standard deviation.

Interval Explorer for One Sample Mean Options

The Explorer red triangle menu and report buttons provide additional options:

Simulate Data

Opens a data table of simulated data based on the explorer settings. View the simulated response column formula for the settings used.

Make Data Collection Table

Creates a new data table that you can use for data collection. The table includes scripts to facilitate data analysis.

Save Settings

Saves the current settings to the Saved Settings table. This enables you to save a set of alternative study plans. See Saved Settings in the Sample Size Explorers.

Help

Opens JMP help.

Statistical Details for the Margin of Error for One Sample Mean Explorer

The calculation for each interval type uses the standard normal-based procedures if σ is known and t distribution procedures or approximations otherwise.

Confidence Intervals

The margin of error (MOE) for confidence intervals is calculated as follows:

Equation shown here

The bound is calculated as follows:

Equation shown here

Prediction Intervals

The margin of error (MOE) for prediction intervals is calculated as follows:

Equation shown here

The bound is calculated as follows:

Equation shown here

Tolerance Intervals

For the tolerance interval on a proportion q of the population, the margin of error or bound is computed based on approximate procedures described in Krishnamoorthy and Mathew (2009).

The margin of error (MOE) for tolerance intervals is calculated as follows:

Equation shown here

The bound is calculated as follows:

Equation shown here

where N is a suitably large integer value to represent asymptotic behavior. JMP sets the value of N to 2000.

Want more information? Have questions? Get answers in the JMP User Community (community.jmp.com).