P Value Calculator From Mean And SD

T-test Formula:

\[ t = \frac{\bar{X} - \mu_0}{s/\sqrt{n}} \]

Sample Mean (X̄):

Sample Standard Deviation (s):

Sample Size (n):

Hypothesized Mean (μ₀):

Test Type:

t-statistic:

P-value:

Degrees of Freedom:

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1. What is a P-value from Mean and SD?

The P-value calculated from mean and standard deviation is a statistical measure that helps determine the significance of results in hypothesis testing. It represents the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.

2. How the Calculator Works

The calculator uses the t-test formula:

\[ t = \frac{\bar{X} - \mu_0}{s/\sqrt{n}} \]

Where:

\( \bar{X} \) — Sample mean
\( \mu_0 \) — 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. The p-value is then calculated from the t-distribution with n-1 degrees of freedom.

3. Interpreting the Results

Details: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, while a large p-value suggests weak evidence against the null hypothesis.

4. Using the Calculator

Tips: Enter the sample mean, standard deviation, sample size, and hypothesized mean. Select the appropriate test type (two-tailed, right-tailed, or left-tailed) based on your hypothesis.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this calculator?
A: Use it when you want to test whether your sample mean is significantly different from a hypothesized population mean, and you only have the sample mean and standard deviation.

Q2: What's the difference between one-tailed and two-tailed tests?
A: A two-tailed test checks for any difference (greater or smaller), while one-tailed tests check specifically for greater (right-tailed) or smaller (left-tailed) values.

Q3: What if my sample size is large?
A: For large samples (n > 30), the t-distribution approximates the normal distribution, but this calculator still uses the t-distribution for accuracy.

Q4: Why does the calculator use t-test instead of z-test?
A: The t-test is more appropriate when the population standard deviation is unknown and estimated from the sample, which is the common case.

Q5: What are common significance levels?
A: Common alpha levels are 0.05, 0.01, and 0.001, representing 5%, 1%, and 0.1% significance levels respectively.