Practice Hypothesis Testing in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A systematic method to decide whether sample data provides enough evidence to reject a claim (null hypothesis) about a population parameter.
Think of a courtroom trial: the null hypothesis (H_0) is 'innocent until proven guilty.' You look at the evidence (data) and ask: 'Is this evidence so strong that it would be very unlikely if the defendant were truly innocent?' If yes, you reject the null hypothesis. If not, you don't have enough evidence to convict—but that doesn't prove innocence.
Example 1
mediumA school claims its students average 75 on standardized tests. A sample of n=36 gives \bar{x}=78 with \sigma=12. Test H_0: \mu=75 vs H_a: \mu>75 at \alpha=0.05.
Example 2
hardA medication is claimed to reduce blood pressure by 10 mmHg on average. A clinical trial with n=49 patients shows \bar{x}=8.2 mmHg reduction, s=7 mmHg. Test H_0: \mu=10 vs H_a: \mu \neq 10 at \alpha=0.05.
Example 3
easyState null and alternative hypotheses for each scenario: (a) testing if a coin is fair, (b) testing if a new drug reduces fever faster than the standard drug.
Example 4
hardA teacher claims students average 80 points. A skeptic samples n=25 students: \bar{x}=76, s=10. Using z = \frac{\bar{x}-\mu_0}{s/\sqrt{n}}, test H_0: \mu=80 vs H_a: \mu < 80 at \alpha=0.01.