Inference and Conclusions Checkpoint
A free Statistics and Data Analysis lesson from the “Inference and Conclusions” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint reviews sampling variability, confidence intervals, hypothesis tests, p-values, error types, chi-square reasoning, and statistical conclusions.
What you'll learn
- Review the major skills from this part of the course
- Choose an appropriate statistical method
- Explain results in context
Worked example
Problem. At alpha = 0.05, a p-value of 0.03 leads to:
- Worked Example: First identify exactly what the question is asking: At alpha = 0.05, a p-value of 0.03 leads to:
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Compare p-value to alpha.
- 0.03 is less than 0.05, so reject the null.
Answer: reject the null hypothesis
Practice problems
1. Review case A: At alpha = 0.05, a p-value of 0.03 leads to:
Choices: ignore the alternative · reject the null hypothesis · fail to reject the null hypothesis · increase the sample size to 0.05
Show solution
- Checkpoint Review: First identify exactly what the question is asking: At alpha = 0.05, a p-value of 0.03 leads to:
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Compare p-value to alpha.
- 0.03 is less than 0.05, so reject the null.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: reject the null hypothesis
2. Review case B: A Type I error means:
Choices: computing the mean · making a scatter plot · rejecting a true null hypothesis · failing to reject a false null hypothesis
Show solution
- Checkpoint Review: First identify exactly what the question is asking: A Type I error means:
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- Type I error is a false alarm.
- It rejects the null when the null is actually true.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: rejecting a true null hypothesis
3. Review case C: Power is the probability of:
Choices: making a Type I error · choosing a bar chart · having no sample variability · detecting a real effect
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Power is the probability of:
- For probability, count favorable outcomes and total outcomes carefully before writing the ratio.
- Power is the chance a test rejects a false null.
- That means it detects a real effect.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: detecting a real effect
4. Review case D: A correct statistical conclusion should include:
Choices: the decision and context · only the formula name · only the answer choice letter · no reference to the problem
Show solution
- Checkpoint Review: First identify exactly what the question is asking: A correct statistical conclusion should include:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- A conclusion must say what the evidence means in context.
- The decision alone is not enough.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: the decision and context
5. Review case E: A chi-square test for a two-way table looks for evidence of:
Choices: a normal percentile · association between categorical variables · a difference in two means · a slope in a scatter plot
Show solution
- Checkpoint Review: First identify exactly what the question is asking: A chi-square test for a two-way table looks for evidence of:
- Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
- Two-way tables contain categorical counts.
- Chi-square tests can check association between the categories.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: association between categorical variables
Practice this interactively with instant feedback and an AI tutor.
Practice Inference and Conclusions Checkpoint Take the free placement check