Hypothesis Testing with One Sample Flashcards
What is the null hypothesis (H₀) in hypothesis testing?
A statement of no effect or no difference; assumed true until evidence suggests otherwise. Includes equality (=, ≤, ≥).
What is the alternative hypothesis (Hₐ)?
The statement that contradicts H₀; represents what you’re trying to prove, using ≠, <, or >.
What is a Type I Error?
Rejecting a true null hypothesis. Probability = α (Level of Significance).
What is a Type II Error?
Failing to reject a false null hypothesis. Probability = β.
What is the Power of a Test?
Probability of correctly rejecting a false null hypothesis. Calculated as 1 − β.
What is a p-value?
Probability of observing the result (or more extreme) assuming the null hypothesis is true.
What does it mean if the p-value < α?
Reject the null hypothesis.
What does it mean if the p-value ≥ α?
Do not reject the null hypothesis.
What is a Confidence Interval (CI)?
A range of values likely to contain a population parameter, based on confidence level, sample size, and variability.
What is the Level of Significance (α)?
The threshold for rejecting the null hypothesis. Common values: 0.01, 0.05, 0.10.
When do you use the t-distribution?
- You are estimating a population mean (or comparing means),
- And the population standard deviation (σ) is unknown,
- And your sample size is small (typically n < 30),
- AND you assume the underlying population is approximately normal (or your sample size is large enough for the Central Limit Theorem to kick in if not).
When do you use the normal distribution in hypothesis testing?
- The population standard deviation (σ) is known,
- Or you have a large sample size (usually n ≥ 30), even if σ is unknown — using the Central Limit Theorem
- And you’re dealing with things like means, proportions, or differences of means/proportions that are expected to behave normally.
Conditions to use a binomial distribution?
Fixed number of trials, independent trials, only two outcomes (success/failure), same probability of success.
Mean (μ) and standard deviation (σ) of a binomial distribution B(n, p)?
Mean: μ = np; Std Dev: σ = √(npq), where q = 1 – p
What does the Central Limit Theorem (CLT) say?
For large n, the sampling distribution of the sample mean approaches a normal distribution.
What is the standard error of the mean?
σ/√n, where σ is the population standard deviation.
What are the steps of a full hypothesis test?
- State H₀ and Hₐ 2. Identify the random variable 3. Choose the distribution 4. Calculate test statistic and p-value 5. Compare p-value with α 6. Decide and conclude
What is a test statistic?
A value (e.g., z or t score) from sample data used to determine the p-value.
Conditions to test a single population proportion?
Random sample, binomial model valid, and both np > 5 and nq > 5.
When is an event considered a rare event in hypothesis testing?
When the probability under the null hypothesis is very low (i.e., small p-value).
