Hypothesis Testing and t-Values

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What is a t-value?

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A t-value is a statistic used in hypothesis testing that measures the size of the difference relative to the variation in your sample data. It is used when the sample size is small (n < 30) or when the population standard deviation is unknown.

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When should you use a t-test instead of a z-test?

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Use a t-test when the sample size is less than 30 (n < 30) or when the population standard deviation is unknown.

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What is the null hypothesis (H0)?

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The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing.

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What is the alternative hypothesis (H1)?

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The alternative hypothesis (H1) is a statement that indicates the presence of an effect or a difference, and it is what the researcher aims to support.

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What does a left-tailed test indicate?

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A left-tailed test is used to determine if the sample mean is significantly less than the population mean. It tests hypotheses of the form H1: x̄ < μ.

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What is the critical value in hypothesis testing?

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The critical value is a threshold that determines whether to reject the null hypothesis. It is based on the significance level (alpha) and the distribution of the test statistic.

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What is the significance level (alpha)?

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The significance level (alpha) is the probability of rejecting the null hypothesis when it is actually true. Common values are 0.05, 0.01, and 0.10.

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What does it mean if a result is statistically significant?

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A result is statistically significant if the p-value is less than the significance level (alpha), indicating strong evidence against the null hypothesis.

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What is a two-tailed test?

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A two-tailed test is used to determine if the sample mean is significantly different from the population mean in either direction (greater or less). It tests hypotheses of the form H1: x̄ ≠ μ.

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How do you calculate the t-value?

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