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One Sample T-Test Formula:
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The one sample t-test is a statistical hypothesis test used to determine whether an unknown population mean is different from a specific value. It compares the mean of your sample data to a known value (the hypothesized population mean).
The calculator uses the one sample t-test formula:
Where:
Explanation: The t-statistic measures how many standard errors the sample mean is from the hypothesized mean. A larger absolute t-value indicates greater evidence against the null hypothesis.
Details: The one sample t-test is widely used in research to test hypotheses about population means 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 (n > 1, s ≥ 0).
Q1: When should I use a one sample t-test?
A: Use it when you want to compare a sample mean to a known value, especially when you don't know the population standard deviation and have a small sample size.
Q2: What's the difference between z-test and t-test?
A: Use z-test when population standard deviation is known (regardless of sample size) or when sample size is large (typically n > 30). Use t-test when population standard deviation is unknown and sample size is small.
Q3: How do I interpret the t-statistic?
A: The larger the absolute value of t, the more evidence against the null hypothesis. Compare your t-value to critical values from the t-distribution table based on your degrees of freedom (n-1) and significance level.
Q4: What are the assumptions of the t-test?
A: The test assumes that the data are approximately normally distributed, observations are independent, and the data are continuous.
Q5: Can I use this for paired samples?
A: No, for paired samples (before/after measurements), you should use a paired t-test which analyzes the differences between pairs.