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One-Tailed T-Test Formula:
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The one-tailed t-test is a statistical test used to determine if there is a significant difference between the mean of a sample and a hypothesized population mean in one specific direction. It tests whether the sample mean is significantly greater than or less than the hypothesized mean.
The calculator uses the one-tailed t-test formula:
Where:
Explanation: The formula calculates how many standard errors the sample mean is away from the hypothesized mean. A larger absolute t-value indicates stronger evidence against the null hypothesis.
Details: The t-statistic is crucial for hypothesis testing in statistics. It helps determine whether to reject the null hypothesis when the population standard deviation is unknown and the sample size is small (typically n < 30).
Tips: Enter the sample mean, hypothesized mean, sample standard deviation, and sample size. All values must be valid (standard deviation > 0, sample size ≥ 1).
Q1: When should I use a one-tailed t-test?
A: Use a one-tailed test when you have a specific directional hypothesis (e.g., testing if a new treatment is better than existing, not just different).
Q2: What is the difference between one-tailed and two-tailed tests?
A: One-tailed tests look for an effect in one direction only, while two-tailed tests detect differences in either direction. One-tailed tests have more statistical power for the specified direction.
Q3: What is a typical critical t-value for significance?
A: Critical values depend on degrees of freedom (n-1) and significance level (typically 0.05). For large samples, values beyond ±1.96 are significant at α=0.05.
Q4: What are the assumptions of the t-test?
A: The test assumes the data are normally distributed, observations are independent, and the sample is randomly selected from the population.
Q5: Can I use this for small sample sizes?
A: Yes, the t-test is specifically designed for small sample sizes (typically n < 30) where the population standard deviation is unknown.