T-Test Calculator | Industrial Engineering Calculators

Student's T-Test

The t-test is a statistical test used to determine if there is a significant difference between the means of two groups or between a sample mean and a known value. It's widely used in hypothesis testing in industrial engineering and quality control applications.

t = (X̄ - μ) / (s / √n)

Where:

X̄ = Sample mean
μ = Population mean (or mean difference for paired tests)
s = Sample standard deviation
n = Sample size

Test Type

Select the type of t-test you want to perform:

One-Sample T-Test

Two-Sample T-Test

Paired T-Test

One-Sample T-Test

Compare the mean of a single sample to a known value or hypothesized mean.

Sample Data (comma-separated values):

Enter numerical values separated by commas. You can also copy and paste from a spreadsheet.

Hypothesized Mean (μ₀):

Significance Level (α):

One-Sample T-Test Results

T-Statistic

Degrees of Freedom

P-Value

Critical Value

Interpretation

Sample Statistics

Statistic	Value
Sample Size (n)
Sample Mean (X̄)
Sample Standard Deviation (s)
Standard Error of Mean
95% Confidence Interval

Two-Sample T-Test

Compare the means of two independent samples to determine if they are significantly different.

Sample 1 Data (comma-separated values):

Sample 2 Data (comma-separated values):

Significance Level (α):

Assume Equal Variances?

Two-Sample T-Test Results

T-Statistic

Degrees of Freedom

P-Value

Critical Value

Interpretation

Sample Statistics

Statistic	Sample 1	Sample 2
Sample Size (n)
Sample Mean (X̄)
Sample Standard Deviation (s)
Standard Error of Mean

Paired T-Test

Compare the means of two related samples (e.g., before and after measurements).

Before Treatment Data (comma-separated values):

After Treatment Data (comma-separated values):

Ensure the order of measurements matches the before treatment data.

Significance Level (α):

Paired T-Test Results

T-Statistic

Degrees of Freedom

P-Value

Critical Value

Interpretation

Difference Statistics

Statistic	Value
Number of Pairs (n)
Mean Difference
Standard Deviation of Differences
Standard Error of Mean Difference
95% CI for Mean Difference

T-Test Examples in Industrial Engineering

Quality Control Example

A manufacturer wants to test if the mean diameter of produced bolts (sample: 10.1, 10.2, 9.9, 10.0, 10.1 mm) is significantly different from the specification of 10.0 mm (one-sample t-test).

Process Improvement Example

An engineer compares the output of two machines (Machine A: 105, 108, 110, 107, 106 units; Machine B: 100, 102, 99, 101, 103 units) to determine if there's a significant difference in productivity (two-sample t-test).

Before-After Study Example

A company measures processing time before (12.5, 13.0, 12.8, 13.2, 12.9 min) and after (11.8, 12.0, 11.7, 12.1, 11.9 min) implementing a new workflow to see if the change significantly reduced processing time (paired t-test).

Understanding T-Test Results

P-Value Range	Interpretation
p ≤ 0.01	Strong evidence against the null hypothesis
0.01 < p ≤ 0.05	Moderate evidence against the null hypothesis
0.05 < p ≤ 0.10	Weak evidence against the null hypothesis
p > 0.10	Little or no evidence against the null hypothesis