What is a p-value?

The probability of obtaining sample data (or more extreme) if the null hypothesis is true.

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What is a p-value?
The probability of obtaining sample data (or more extreme) if the null hypothesis is true.
What is the null hypothesis (H0)?
A statement of no effect or no difference, which we try to disprove.
What is the alternative hypothesis (Ha)?
A statement that contradicts the null hypothesis, representing what we are trying to find evidence for.
Define significance level (alpha).
The probability of rejecting the null hypothesis when it is actually true (Type I error).
What is a confidence interval?
A range of values, calculated from sample data, that is likely to contain the true population parameter.
Explain the concept of Type I error.
Rejecting the null hypothesis when it is actually true (false positive).
Explain the concept of Type II error.
Failing to reject the null hypothesis when it is actually false (false negative).
Explain what 'statistical significance' means.
The observed effect is unlikely to have occurred by random chance alone, assuming the null hypothesis is true.
Explain the purpose of checking conditions (Random, Independent, Normal) before performing inference.
To ensure the sampling distribution is approximately normal and that the results of the test/interval are valid.
What does it mean to 'fail to reject the null hypothesis'?
There is not enough evidence to conclude that the alternative hypothesis is true. It does *not* mean the null hypothesis is true.
What are the differences between a one-sample t-test and a two-sample t-test?
One-sample: Compares a sample mean to a known value. | Two-sample: Compares the means of two independent groups.
What are the differences between a two-sample t-test and a matched pairs t-test?
Two-sample: Compares means of independent groups. | Matched pairs: Compares means of related groups (e.g., before/after).
What are the differences between a t-test and a z-test?
T-test: Used when the population standard deviation is unknown, estimate using sample std. dev. | Z-test: Used when the population standard deviation is known.
What are the differences between a significance test and a confidence interval?
Significance test: Determines if there is evidence to reject a null hypothesis. | Confidence interval: Estimates a range of plausible values for a population parameter.
What are the differences between the conditions for inference for means and proportions?
Means: Random, Independent, Normal (or large sample size). | Proportions: Random, Independent, Large Counts (np ≥ 10 and n(1-p) ≥ 10).