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What are the differences between a one-sample t-test and a two-sample t-test?
One-sample: Compares the mean of a single sample to a known value. | Two-sample: Compares the means of two independent samples.
What are the differences between rejecting the null hypothesis and failing to reject the null hypothesis?
Reject: Sufficient evidence to support the alternative hypothesis. | Fail to reject: Not enough evidence to support the alternative hypothesis.
What are the differences between using a t-table and technology to find the p-value?
T-table: Provides a range for the p-value based on degrees of freedom and t-score. | Technology: Provides a precise p-value, t-score, and degrees of freedom.
What is the formula for the two-sample t-test statistic?
$\text{t} = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}$
How do you calculate degrees of freedom (df) by hand?
df = min(n1 - 1, n2 - 1)
What is the general form for calculating a test statistic?
(Observed Difference) / (Standard Error) which is essentially (sample statistic - null hypothesis value) / (standard error of the statistic)
What is a two-sample t-test?
A test to determine if there is a statistically significant difference between the means of two independent groups.
Define 'degrees of freedom' (df) in a t-test.
The number of independent pieces of information available to estimate a parameter. Approximated as min(n1-1, n2-1) for two-sample t-tests by hand.
What is a p-value?
The probability of observing a sample mean difference as extreme as, or more extreme than, what you got, assuming the null hypothesis is true.
Define 'significance level' (ฮฑ).
The probability of rejecting the null hypothesis when it is true (Type I error).
What is the null hypothesis (H0)?
A statement of no effect or no difference, which we aim to disprove.
What is the alternative hypothesis (Ha)?
A statement that contradicts the null hypothesis, representing what we are trying to find evidence for.