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What is the formula for a t-score?
$t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$
How do you calculate degrees of freedom (df) for a one-sample t-test?
$df = n - 1$
What is the definition of a t-score?
A test statistic indicating how many standard errors away a sample mean is from the hypothesized population mean.
What is the definition of a p-value?
The probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
Define a one-tailed test.
A hypothesis test where the alternative hypothesis is directional (e.g., μ > X or μ < X).
Define a two-tailed test.
A hypothesis test where the alternative hypothesis is non-directional (e.g., μ ≠ X).
What are degrees of freedom (df)?
The number of independent pieces of information available to estimate a parameter. In a one-sample t-test, df = n - 1.
Explain the concept of a t-test.
A t-test is used to determine if there is a statistically significant difference between the sample mean and a hypothesized population mean.
Explain the concept of using the t-table to find p-values.
The t-table provides a range for the p-value based on the t-score and degrees of freedom. Locate your t-score using the correct df to estimate the p-value.
Explain the concept of drawing conclusions using p-values.
Compare the p-value to the significance level (α). If p < α, reject the null hypothesis. If p > α, fail to reject the null hypothesis.
Explain the concept of Type I error related to one-tailed tests.
A one-tailed test carries a higher risk of Type I error if the direction of the alternative hypothesis is wrong.
Explain the importance of context when interpreting t-test results.
Always interpret your results in the context of the problem. Explain what the t-score and p-value mean in relation to the data and research question.