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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 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.
What is the general form of a confidence interval?
Point estimate ± (Critical value * Standard error)
What is the test statistic for a one-sample t-test?
$t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$
What is the test statistic for a one-sample z-test for proportions?
$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$
What is the formula for degrees of freedom in a matched pairs t-test?
df = n - 1, where n is the number of pairs.
What is the general form for a test statistic?
$\frac{statistic - parameter}{standard \ error \ of \ the \ statistic}$