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T-Test Statistic Formula:
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The t-test statistic measures how many standard errors the sample mean is away from the population mean. It's used in hypothesis testing to determine if there's a significant difference between sample and population means.
The calculator uses the t-test statistic formula:
Where:
Explanation: The formula calculates how far the sample mean deviates from the population mean in terms of standard error units.
Details: The t-statistic is crucial for conducting t-tests, which help determine if observed differences between sample and population are statistically significant or due to random chance.
Tips: Enter sample mean, population mean, standard deviation, and sample size. Standard deviation must be greater than 0, and sample size must be at least 2.
Q1: When should I use a t-test?
A: Use t-tests when comparing sample means to population means, especially with small sample sizes (n < 30) or when population standard deviation is unknown.
Q2: What does the t-value represent?
A: The t-value represents how many standard errors the sample mean is above or below the population mean. Larger absolute t-values indicate greater evidence against the null hypothesis.
Q3: How is t-value different from z-score?
A: Both measure standard deviations from mean, but t-test uses sample standard deviation while z-test uses population standard deviation. T-test is more appropriate for small samples.
Q4: What is a good t-value?
A: There's no "good" or "bad" t-value - it depends on your significance level and degrees of freedom. Typically, |t| > 2 indicates potential significance for moderate sample sizes.
Q5: Can I use this for one-sample t-test?
A: Yes, this calculator provides the test statistic for a one-sample t-test comparing a sample mean to a known population mean.