H0 and H1
H0 usually states no effect or no difference. H1 states the research direction or difference being tested.
Statistics practice quiz for hypothesis testing
Hypothesis Testing Quiz
Practice null and alternative hypotheses, p-values, alpha, Type I and Type II errors, one-tailed and two-tailed tests, confidence interval decisions, and conclusion wording with original statistics quiz questions.
- 24 original practice questions
- P-values, alpha, errors, tails, power, and conclusions
- Beginner, intermediate, and advanced filters
- Full visible answer library for review
Reviewed for Statskan: original hypothesis testing scenarios, answer explanations, and calculator links. Last reviewed: July 2026.
- Hypotheses Practice H0, H1, direction, and research-claim wording.
- P-values Review correct p-value interpretation and decision rules.
- Errors Separate Type I error, Type II error, alpha, beta, and power.
- Conclusions Write reject or fail-to-reject decisions without overclaiming.
How to Think About Hypothesis Testing
Quick answer: State H0 and H1, choose alpha before the test, calculate
or read the p-value, compare p with alpha, then write the decision in context without
claiming the null hypothesis has been proven true.
Hypothesis testing is one of the most common sources of statistics homework mistakes. Students often know the formula but lose points on the alternative hypothesis, tail direction, p-value interpretation, or final conclusion wording.
Practice Hypothesis Testing
Filter by topic or level, answer each question, and review the explanation after choosing.
Hypotheses
Question 1 of 24
In a hypothesis test, what does the null hypothesis usually represent?
Hypothesis Testing Study Guide
Review these concepts before reading software output or writing a conclusion.
Alpha and p-values
Alpha is the cutoff. The p-value is compared with alpha to decide whether evidence is strong enough to reject H0.
One-tailed vs two-tailed
Use one-tailed tests for directional claims and two-tailed tests when either direction matters.
Errors and power
Type I error rejects a true H0. Type II error fails to reject a false H0. Power detects real effects.
Confidence intervals
For many two-tailed tests, a matching confidence interval excluding the null value agrees with rejection.
Conclusion wording
Write the decision in context and avoid saying the null hypothesis is proven true.
Need Help With a Hypothesis Testing Assignment?
Send the full prompt, data or summary statistics, required test, alpha level, software output, and deadline. Statskan can help explain the p-value, decision, assumptions, and conclusion.
Hypothesis Testing Question Library
The full question and answer library is visible so students and search engines can read the practice content without relying on JavaScript.
Question 1
In a hypothesis test, what does the null hypothesis usually represent?
Answer: The claim of no effect, no difference, or no association
The null hypothesis, often written as H0, usually represents no change, no difference, no relationship, or the default claim being tested against.
Question 2
A tutoring program is expected to increase average quiz scores. Which alternative hypothesis direction fits this claim?
Answer: Greater than
If the claim is an increase, the alternative hypothesis is right-tailed and uses a greater-than direction.
Question 3
A researcher only wants to know whether a mean changed, with no predicted direction. Which alternative hypothesis is most appropriate?
Answer: Not equal to
A two-tailed alternative uses not equal to when the research question asks whether a value changed in either direction.
Question 4
What does alpha represent in hypothesis testing?
Answer: The significance level used as the decision cutoff
Alpha is the significance level, often 0.05, used as the cutoff for deciding whether the p-value is small enough to reject H0.
Question 5
If p = 0.03 and alpha = 0.05, what is the correct decision?
Answer: Reject the null hypothesis
Because 0.03 is less than 0.05, the result is statistically significant at the 5% level, so H0 is rejected.
Question 6
If p = 0.08 and alpha = 0.05, what is the correct decision?
Answer: Fail to reject the null hypothesis
Because 0.08 is greater than 0.05, the evidence is not strong enough to reject H0 at the 5% level.
Question 7
Which sentence is the best interpretation of a p-value?
Answer: The probability of getting results this extreme or more extreme if the null hypothesis is true
A p-value is calculated under the assumption that H0 is true. It is not the probability that H0 itself is true.
Question 8
A student writes, "p = 0.02 means there is a 2% chance the null hypothesis is true." What is wrong?
Answer: A p-value is not the probability that H0 is true
The p-value describes how unusual the sample result would be assuming H0 is true; it does not directly assign a probability to H0.
Question 9
A manufacturer claims a battery lasts longer than 12 hours. Which tail direction is most appropriate?
Answer: Right-tailed test
The claim "longer than" points to values greater than 12, so the alternative hypothesis is right-tailed.
Question 10
A researcher tests whether a new process reduces average wait time. Which tail direction fits the alternative hypothesis?
Answer: Left-tailed test
A reduction means the alternative hypothesis points below the old mean, so the test is left-tailed.
Question 11
A researcher tests whether average sleep hours differ from 7 hours, without predicting higher or lower. Which test direction fits?
Answer: Two-tailed test
The word "differ" without a direction indicates a two-tailed test, because either higher or lower values matter.
Question 12
What is a Type I error?
Answer: Rejecting a true null hypothesis
A Type I error is a false positive: the test rejects H0 even though H0 is actually true.
Question 13
What is a Type II error?
Answer: Failing to reject a false null hypothesis
A Type II error is a false negative: the test does not reject H0 even though the alternative is actually true.
Question 14
What does statistical power measure?
Answer: The probability of detecting an effect when the effect really exists
Power is the probability of correctly rejecting a false H0. Higher power means a lower chance of Type II error.
Question 15
All else equal, what usually happens when sample size increases?
Answer: Power increases
Larger samples usually make effects easier to detect, which increases statistical power when other conditions are held constant.
Question 16
Which conclusion wording is safest after failing to reject H0?
Answer: There is not enough evidence to support the alternative hypothesis
Failing to reject H0 means the evidence was not strong enough. It does not prove that H0 is true.
Question 17
A result is statistically significant but the mean difference is extremely small. What should the student consider?
Answer: Practical significance
Statistical significance does not automatically mean the result is important in the real world. Practical significance and effect size should also be considered.
Question 18
For a two-tailed test at alpha = 0.05, a 95% confidence interval for a mean difference does not include 0. What does that usually suggest?
Answer: Reject H0 at the 0.05 level
For many two-tailed tests, if the 95% confidence interval for a difference excludes the null value, the result is significant at alpha = 0.05.
Question 19
A 95% confidence interval for a mean difference includes 0. What does this usually suggest for a two-tailed test at alpha = 0.05?
Answer: Fail to reject H0
If a confidence interval for a difference includes the null value of 0, the corresponding two-tailed test is usually not significant at the matching alpha level.
Question 20
What does a test statistic generally measure?
Answer: How far the sample result is from the null value in standardized units
A test statistic such as z, t, chi-square, or F summarizes how far the observed data are from what H0 predicts.
Question 21
Which pair is commonly reported for a t-test conclusion?
Answer: t statistic and p-value
A t-test report commonly includes the t statistic, degrees of freedom, p-value, and sometimes a confidence interval or effect size.
Question 22
Why should assumptions be checked before interpreting a hypothesis test?
Answer: Because the validity of the p-value can depend on the test assumptions
Assumptions such as independence, normality, equal variance, or expected counts affect whether the chosen test and p-value are appropriate.
Question 23
Why is it risky to choose alpha after seeing the p-value?
Answer: It can make the decision biased and inflate false-positive risk
Alpha should be chosen before the test. Changing the cutoff after seeing the result can make the analysis misleading.
Question 24
A student runs many tests and only reports the one with p < 0.05. What is the main concern?
Answer: Selective reporting can inflate the chance of a false positive
Running many tests and reporting only significant results can make random patterns look meaningful unless the analysis plan and multiple-testing issue are handled carefully.
Related Statistics Help
Use Practice Quizzes Responsibly
Use this quiz to review concepts, prepare questions, and understand hypothesis testing. For graded work, follow your institution academic-integrity rules and use support in a way you can explain.