10. Significance Tests and Statistical Inference Free Online FlashCards

What is the goal of a significance test?

A significance test uses sample data to evaluate a claim about a population parameter by comparing the observed result with what would be expected if the null hypothesis were true.

What does the null hypothesis represent?

The null hypothesis, H₀, is the baseline claim, usually representing no change, no difference, or a specified population value. It includes equality.

What determines whether a test is one- or two-sided?

The alternative hypothesis identifies the research claim and determines whether evidence is sought in one direction or in both directions.

What are the four steps of a significance test?

The four steps are: state H₀ and Hₐ, calculate a test statistic, find and interpret the p-value, and make a decision and contextual conclusion.

What is the general form of a test statistic?

test statistic = (observed statistic − null value) / standard error under H₀. It measures the distance from the null relative to sampling variability.

What is the one-proportion z test statistic?

For one population proportion, z = (p̂ − p₀) / √[p₀(1 − p₀)/n], where p̂ is the sample proportion and p₀ is the null value.

What conditions support a one-proportion normal test?

The usual normal approximation requires a random or representative sample and expected null counts satisfying np₀ ≥ 10 and n(1 − p₀) ≥ 10.

What statistic tests one population mean when σ is unknown?

When the population standard deviation is unknown, use t = (x̄ − μ₀)/(s/√n), with n − 1 degrees of freedom.

What does a p-value measure?

A p-value is the probability, assuming H₀ is true, of obtaining the observed test statistic or one more extreme in the direction specified by Hₐ.

What does a p-value not tell you?

A p-value is not the probability that H₀ is true, that Hₐ is true, or that the result occurred by “random chance alone.” It also does not measure effect size.

What is the p-value decision rule?

If p-value ≤ α, reject H₀; if p-value > α, fail to reject H₀. “Fail to reject” does not mean that H₀ has been proven true.

What is a Type I error?

A Type I error occurs when a true null hypothesis is rejected. Its probability is α, the chosen significance level.