Hypothesis Test vs Confidence Interval
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Hypothesis test
Hypothesis testing
A hypothesis test uses sample data to weigh a null claim against an alternative, gauging how surprising the data would be if the null claim were true.
A significance test decides whether the evidence in a sample is strong enough to reject a default claim about a parameter. You state a null and an alternative hypothesis, compute a test statistic, and find its p-value under the null. For example, to test whether a coin is fair you compare the observed number of heads to what a fair coin predicts. If the p-value is at or below the significance level, you reject the null hypothesis; otherwise you fail to reject it.
Confidence interval
Confidence intervals
A confidence interval is a range of plausible values for a population parameter, built from a sample as the estimate plus or minus a margin of error.
A confidence interval gives a range for an unknown population parameter instead of a single guess, acknowledging that samples vary. Its width reflects the uncertainty in the estimate: more data and less spread give a narrower interval. For example, a 95% confidence interval of 52% plus or minus 3% for support runs from 49% to 55%. The general form is , where the standard error measures the typical size of sampling error.