1. What is the Simple T Test?

The simple t-test (or one-sample t-test) compares the mean of a sample to a known value (the hypothesized population mean) to determine if the sample mean is significantly different from the hypothesized mean.

2. How Does the Calculator Work?

The calculator uses the t-test formula:

Where:

• \( x \) — Sample mean
• \( \mu \) — Hypothesized population mean
• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The t-statistic measures how many standard errors the sample mean is from the hypothesized mean.

3. Importance of T Test Calculation

Details: The t-test is fundamental in hypothesis testing, allowing researchers to determine if observed differences are statistically significant or likely due to chance.

4. Using the Calculator

Tips: Enter the sample mean, hypothesized mean, sample standard deviation, and sample size. All values must be valid (n > 0, s ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a t-test instead of a z-test?
A: Use a t-test when the population standard deviation is unknown and the sample size is small (typically n < 30).

Q2: What does the t-statistic tell me?
A: The t-statistic indicates how far the sample mean deviates from the hypothesized mean in standard error units. Larger absolute values suggest stronger evidence against the null hypothesis.

Q3: What are degrees of freedom in a t-test?
A: For a one-sample t-test, degrees of freedom = n - 1. This affects the shape of the t-distribution used to determine p-values.

Q4: What's a good sample size for a t-test?
A: While t-tests can work with small samples (n ≥ 5), larger samples (n ≥ 30) provide more reliable results.

Q5: How do I interpret the t-statistic?
A: Compare your t-statistic to critical values from the t-distribution table. If |t| > critical value, the result is statistically significant.