CalculateConfidenceIntervalOfMean

Introduction

A sample mean is a point estimate, not the truth — the real question is how far off it could plausibly be from the population mean it's standing in for. CalculateConfidenceIntervalOfMean answers that from summary statistics alone: it computes a confidence interval for the population mean, automatically choosing the t-distribution for small samples (n < 30) or the z-distribution for larger ones, and optionally plots the inferred sampling distribution so the width of the uncertainty is visible, not just a printed range.

Teaching Note

Calculating confidence intervals is essential for:

Estimating population parameters from sample data with quantified uncertainty.
Epidemiology: Determining the mean incubation period of a pathogen in a clinical study.
Healthcare: Assessing the average reduction in blood pressure across a patient cohort.
Intelligence Analysis: Estimating the mean frequency of communication events from a monitored source.
Data Science: Evaluating the average processing time of a distributed system.
Quality Control: Monitoring the mean weight or dimensions of manufactured components.
Finance: Estimating the average daily return of an asset over a specific period.
Social Science: Analyzing the mean response score from a public opinion survey.

Parameters

Parameter	Type	Default	Description
`sample_mean`required	`float`	—	The arithmetic mean observed in the sample data.
`sample_sd`required	`float`	—	The standard deviation of the sample, used to estimate the population standard deviation.
`sample_size`required	`int`	—	The number of observations in the sample. This determines whether a t-stat or z-stat is used.
`confidence_interval`	`float`	`0.95`	The desired confidence level, expressed as a decimal between 0 and 1. Defaults to 0.95.
`plot_sample_distribution`	`bool`	`True`	Whether to generate and display a histogram showing the inferred sampling distribution of the mean. Defaults to True.
`value_name`	`str`	`'Possible Mean'`	A descriptive name for the variable being analyzed, used as the x-axis label in the plot. Defaults to 'Possible Mean'.
`fill_color`	`str`	`'#999999'`	The hex color code for the bars in the distribution plot. Defaults to '#999999'.
`fill_transparency`	`float`	`0.6`	The alpha transparency level for the plot's histogram bars (0 to 1). Defaults to 0.6.
`title_for_plot`	`str`	`'Confidence Interval of Mean'`	The primary title text displayed at the top of the plot. Defaults to 'Confidence Interval of Mean'.
`subtitle_for_plot`	`str`	`'Shows the distribution of the sample mean.'`	Descriptive subtitle text displayed below the main title.
`caption_for_plot`	`str`	`None`	An optional descriptive caption or note displayed at the bottom of the plot. Defaults to None.
`data_source_for_plot`	`str`	`None`	Text indicating the source of the data, appended to the caption. Defaults to None.
`show_y_axis`	`bool`	`False`	Whether to display the frequency/density scale on the y-axis. Defaults to False.
`title_y_indent`	`float`	`1.1`	Vertical position offset for the plot title. Defaults to 1.10.
`subtitle_y_indent`	`float`	`1.05`	Vertical position offset for the plot subtitle. Defaults to 1.05.
`caption_y_indent`	`float`	`-0.15`	Vertical position offset for the plot caption. Defaults to -0.15.
`figure_size`	`tuple`	`(8, 6)`	The dimensions of the output figure as a (width, height) tuple in inches. Defaults to (8, 6).

Returns

None — the function prints the calculated confidence interval to the console and displays a plot if plot_sample_distribution is True.

Example

python

from analysistoolbox.statistics import CalculateConfidenceIntervalOfMean

# Epidemiology: estimating mean recovery time for a viral infection
CalculateConfidenceIntervalOfMean(
    sample_mean=14.2,
    sample_sd=3.5,
    sample_size=45,
    confidence_interval=0.99,
    value_name="Days to Recovery",
    title_for_plot="99% CI for Mean Recovery Time"
)