What are the differences between the null and alternative hypotheses?
Null Hypothesis: Statement we are trying to find evidence against, assumes no effect. | Alternative Hypothesis: Statement we are trying to support, contradicts the null hypothesis.
What are the differences between a one-tailed and a two-tailed test?
One-tailed Test: Tests for a change in one direction (either > or <). | Two-tailed Test: Tests for a change in either direction (≠).
What is the Null Hypothesis (H0)?
The statement we're trying to find evidence *against*. It's our initial assumption about the population parameter, written as p = [some value].
What is the Alternative Hypothesis (Ha)?
The claim that contradicts the null hypothesis, written as p < [some value], p > [some value], or p ≠ [some value].
What is a one-tailed test?
A test where the alternative hypothesis uses < or >, indicating interest in a change in one direction only.
What is a two-tailed test?
A test where the alternative hypothesis uses ≠, indicating interest in a change in either direction.
What is the p-value?
The probability of getting a sample proportion as extreme as (or more extreme than) ours, assuming the null hypothesis is true.
Explain the concept of the 10% condition.
The 10% condition ensures independence when sampling without replacement. Verify that the population is at least 10 times the size of the sample.
Explain the concept of the Large Counts Condition.
The Large Counts Condition proves that the sampling distribution is approximately normal. Both the expected number of successes (np) and failures (n(1-p)) must be at least 10.
Explain the importance of random sampling in hypothesis testing.
Random sampling is crucial to make inferences about the population. A biased sample renders the results unreliable and invalid.
Explain Type I error.
A Type I error occurs when we reject the null hypothesis when it is actually true.
Explain Type II error.
A Type II error occurs when we fail to reject the null hypothesis when it is actually false.
