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Estimate one population proportion from a random sample, check the conditions that justify a normal interval, calculate the margin of error, and interpret the confidence statement in context.
Estimate a population mean when the population standard deviation is unknown, using the sample standard deviation, a t critical value, and conditions that support the procedure.
Estimate the difference between two population proportions while preserving group order, using separate sample proportions in the standard error and interpreting the interval in context.
Build a significance test from the statistical question outward: define the parameter, write hypotheses, verify the procedure, measure evidence, and make a contextual conclusion without overstating what the data prove.
Translate a research claim into hypotheses about a population parameter, put equality in the null hypothesis, choose the alternative direction before seeing the data, and keep sample statistics out of the hypotheses.
Connect decisions in a significance test to their possible consequences: a Type I error rejects a true null, a Type II error fails to reject a false null, and power is the probability of detecting a specified real effect.
Test a claim about one population proportion using the null value in the standard error, match the p-value tail to the alternative hypothesis, and state the conclusion about the population parameter.
Separate three linked but different ideas: the test statistic measures how far the sample result is from the null model, the p-value measures tail evidence under that model, and alpha supplies the decision threshold.
Use a two proportion z test when two independent groups produce binary outcomes and the question asks whether their population proportions differ or differ in a specified direction. The equality null pools the two samples because the null model treats them as sharing one population proportion.
Use a one sample t test to test a claim about one population mean when the population standard deviation is unknown. The procedure standardizes the distance between the sample mean and the null mean with s divided by the square root of n and evaluates that distance on a t distribution.