Test Statistic Calculator

Test Statistic Formula:

\[ t = \frac{x - \mu}{s / \sqrt{n}} \]

Test Statistic (t):

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1. What is the Test Statistic?

The test statistic (t) measures how far the sample mean deviates from the population mean in terms of standard error units. It's used in hypothesis testing to determine whether to reject the null hypothesis.

2. How Does the Calculator Work?

The calculator uses the test statistic formula:

\[ t = \frac{x - \mu}{s / \sqrt{n}} \]

Where:

\( x \) — Sample mean
\( \mu \) — Population mean
\( s \) — Sample standard deviation
\( n \) — Sample size

Explanation: The numerator measures the difference between sample and population means, while the denominator standardizes this difference by the standard error of the mean.

3. Importance of Test Statistic

Details: The test statistic is crucial for determining statistical significance in hypothesis testing. It helps quantify how extreme the observed results are under the null hypothesis.

4. Using the Calculator

Tips: Enter all required values (sample mean, population mean, sample standard deviation, and sample size). The calculator will compute the t-value which can then be compared to critical values from the t-distribution.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test statistic?
A: Use this when performing a one-sample t-test to compare a sample mean to a known population mean, especially when the population standard deviation is unknown.

Q2: What does a large t-value indicate?
A: A large absolute t-value suggests the sample mean is significantly different from the population mean, potentially leading to rejection of the null hypothesis.

Q3: How does sample size affect the t-value?
A: Larger sample sizes (n) decrease the standard error, which can increase the t-value if the difference between means remains constant.

Q4: What are the assumptions for this test?
A: The data should be approximately normally distributed, especially for small sample sizes, and observations should be independent.

Q5: How do I interpret the t-value?
A: Compare your calculated t-value to critical values from the t-distribution table with n-1 degrees of freedom to determine statistical significance.