What does hypothesis testing involve?
Weighing evidence for two competing claims about a population parameter.
What is the Null Hypothesis ($H_0$)?
The assumption of ‘no effect’ or ‘no difference’ which always contains an equality sign ($=$, $\le$, or $\ge$).
What is the Alternative Hypothesis ($H_1$ or $H_a$)?
The ‘research hypothesis’ or claim you are trying to find evidence for; it always contains an inequality sign ($\ne$, $<$, or $>$).
What is the decision rule regarding p-values?
Reject $H_0$ if the p-value is $\le$ the significance level ($\alpha$); otherwise fail to reject $H_0$.
How is the P-value defined?
The probability of obtaining results as extreme as the observed ones assuming $H_0$ is true.
What is a Type I error?
Rejecting the null hypothesis ($H_0$) when it is actually true.
What is the common term and probability for a Type I error?
It is a ‘False Positive’ with a probability of $\alpha$ (the significance level).
What is a Type II error?
Failing to reject the null hypothesis ($H_0$) when it is actually false.
What is the common term and probability for a Type II error?
It is a ‘False Negative’ with a probability of $\beta$.
What is the Power of a Test ($1 - \beta$)?
The probability of correctly rejecting a false null hypothesis.
How can you increase the Power of a Test?
By using larger sample sizes and larger significance levels ($\alpha$).
What is the purpose of a Confidence Interval?
To use sample data to create a range of values where the true population parameter likely lies.
How does the confidence level affect the interval width?
A higher confidence level (e.g. 99% vs 95%) makes the interval wider.
What is the definition of Margin of Error (ME)?
Half the total width of the confidence interval.
How can you decrease the Margin of Error to make an estimate more precise?
Increase the sample size ($n$) or decrease the confidence level.
What is the formula for Margin of Error?
$ME = (\text{Critical Value}) \times (\text{Standard Error})$.
When should you use the Standard Normal ($Z$) distribution?
When the population standard deviation ($\sigma$) is known.
When should you use the Student’s $t$ distribution?
When the population standard deviation ($\sigma$) is unknown and the sample standard deviation ($s$) is used instead.
What is the formula for Degrees of Freedom ($df$) in a single sample $t$-test?
$df = n - 1$.
