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T-Test Statistic Formula:
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The observed t-test statistic measures how many standard errors the sample mean is away from the hypothesized population mean. It's used in hypothesis testing to determine if there's a statistically significant difference between sample and population means.
The calculator uses the t-test statistic formula:
Where:
Explanation: The formula calculates how many standard errors the sample mean deviates from the population mean, providing a standardized measure of difference.
Details: The t-statistic is crucial for hypothesis testing in statistics. It helps determine whether to reject the null hypothesis and is used in various statistical tests including one-sample t-tests and confidence interval estimation.
Tips: Enter the sample mean, population mean, sample standard deviation, and sample size. All values must be valid (standard deviation > 0, sample size > 1).
Q1: When should I use a t-test statistic?
A: Use it when comparing a sample mean to a known population mean, especially when the population standard deviation is unknown and sample size is small.
Q2: What does a large t-value indicate?
A: A large absolute t-value indicates a greater difference between the sample mean and population mean, suggesting stronger evidence against the null hypothesis.
Q3: How is the t-statistic different from z-statistic?
A: The t-statistic is used when population standard deviation is unknown and estimated from sample data, while z-statistic is used when population standard deviation is known.
Q4: What are the assumptions for using t-test?
A: The data should be approximately normally distributed, observations should be independent, and the sample should be randomly selected.
Q5: How do I interpret the t-statistic value?
A: Compare the calculated t-value to critical values from the t-distribution table with n-1 degrees of freedom to determine statistical significance.