AP Statistics Unit 7: Inference for Quantitative Data: Means

Unit 7 covers inference for means: t-intervals and t-tests for one sample, two samples and paired data. Recognising paired data is the distinction that decides which procedure applies.

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63 questions10 CED topics100% with a figure
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What 63 questions on it look like

It spans 10 CED topics, which is wide enough that "I've studied this unit" is not a meaningful statement. Track your accuracy by topic, not by unit.

100% of the questions come with a figure — a graph, diagram or data display. Reading the figure correctly is most of the work before any content knowledge applies.

Setting Up a Test for a Population Mean17
Setting Up a Test for the Difference of Two Population Means17
Carrying Out a Test for the Difference of Two Population Means13
Constructing a Confidence Interval for a Population Mean6
Justifying a Claim About a Population Mean Based on a Confidence Interval2
Justifying a Claim About the Difference of Two Means Based on a Confidence Interval2
Confidence Intervals for the Difference of Two Means2
Carrying Out a Test for a Population Mean2

Questions per CED topic, top 8 of 10.

From the bank

Three real inference for quantitative data: means questions

Drawn from the practice pool, not from the mock papers.

Setting Up a Test for a Population Mean · Selecting Statistical Methods · with figure

The same 24 students take a diagnostic test before and after a review workshop. The teacher wants to test whether the mean score changed. Which inference procedure is most appropriate?

  1. AA paired t test using each student's after-minus-before differencecorrect
  2. BA chi-square test for independence
  3. CA z procedure is required whenever the sample was randomly selected.
  4. DA one-proportion z test
  5. EA two-sample t test comparing before scores to after scores as independent groups
Why A is correct

The before and after scores are paired because each student contributes two linked measurements. The correct quantitative inference procedure is a paired t test on the within-student differences.

Choosing a paired t procedure: in the "The same 24 students take a diagnostic test before and after a review workshop. The teacher wants to test whether the mean score changed. Which inference procedure is most appropriate?" setting, especially The same 24 students take a diagnostic test before and after a review workshop., choose the method that matches the wording of the stem and justify it with context. The professional check is to keep the values 24, the procedure selection paired t method, and the final answer choice aligned with Inference for Quantitative Data: Means.

Common mistakes. For the stem cue "The same twenty four students take a diagnostic test before and after a review workshop. The teacher wants to test whether the mean score changed. Which inference procedure is most appropriate?", a likely mistake is the response variable is a quantitative score, not a single proportion. Keep the calculation or conclusion tied to the original context.

Setting Up a Test for the Difference of Two Population Means · Selecting Statistical Methods · with figure

A study tests a difference in means for difference in mean wait times. Which hypotheses use the correct parameter?

  1. AH0: xbar_A - xbar_B = 0; Ha: xbar_A - xbar_B != 0
  2. BH0: sample statistic = 0; Ha: sample statistic differs
  3. CH0: mu_A - mu_B = 0; Ha: mu_A - mu_B != 0correct
  4. DH0: p-hat = 0; Ha: x-bar != 0
  5. EH0: mu_A - mu_B != 0; Ha: mu_A - mu_B = 0
Why C is correct

The hypotheses should be H0: mu_A - mu_B = 0 and Ha: mu_A - mu_B != 0.

hypotheses for difference in mean wait times: in the "A study tests a difference in means for difference in mean wait times. Which hypotheses use the correct parameter?" setting, especially difference in mean wait times; mu A - mu B; mu A - mu B = 0, state the hypotheses, compute the relevant test evidence, and conclude in context. The professional check is to keep the values 0, the hypothesis setup method, and the final answer choice aligned with Inference for Quantitative Data: Means.

Common mistakes. For the stem cue "A study tests a difference in means for difference in mean wait times. Which hypotheses use the correct parameter?", a likely mistake is hypotheses should use population parameters, not sample statistics. Keep the calculation or conclusion tied to the original context.

Carrying Out a Test for the Difference of Two Population Means · Statistical Argumentation · with figure

Which statement describes a Type II error for missed difference in mean times?

  1. ACorrectly deciding when the true mean times differ.
  2. BA z procedure is appropriate whenever the sample is random, even when the population standard deviation is unknown.
  3. Cfailing to find evidence of a difference when the true mean times differ.correct
  4. DUsing a sample size that is too large.
  5. EChanging alpha after seeing the data.
Why C is correct

Type II error means failing to reject a false null hypothesis: failing to find evidence of a difference when the true mean times differ.

Type II error for missed difference in mean times: in the "Which statement describes a Type II error for missed difference in mean times?" setting, especially missed difference in mean times; Type II; the true mean times differ, choose the method that matches the wording of the stem and justify it with context. The professional check is to keep the values 2, the type error method, and the final answer choice aligned with Inference for Quantitative Data: Means.

Common mistakes. For the stem cue "Which statement describes a Type II error for missed difference in mean times?", a likely mistake is this is a correct decision, not an error. Keep the calculation or conclusion tied to the original context.

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FAQ

Inference for Quantitative Data: Means questions

When do I use a paired t-test?

When each observation in one group is naturally matched to one in the other — before and after on the same subject, for instance.

Why t rather than z?

Because the population standard deviation is unknown and estimated from the sample, which adds uncertainty the t-distribution accounts for.
Last reviewed 2026-08-28. Unit and topic names follow the College Board course framework. Question counts describe the PrepScore practice bank, not the exam.
Same course
Unit 1: Exploring One-Variable Data460 questionsUnit 2: Exploring Two-Variable Data295 questionsUnit 3: Collecting Data190 questionsUnit 4: Probability, Random Variables, and Probability Distributions100 questionsUnit 5: Sampling Distributions70 questionsUnit 6: Inference for Categorical Data: Proportions107 questionsUnit 9: Inference for Quantitative Data: Slopes133 questions

Practise inference for quantitative data: means until the reasoning is automatic.

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