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AP® Statistics Unit 7 Review and Practice Test

Inference for Quantitative Data: Means

Build your confidence in analyzing sample means and interpreting the results. Explore AP® Stats Unit 7 practice questions and explanations to sharpen your statistical reasoning for the AP® exam.

Master AP Statistics Unit 7 with Expert-Guided Practice

Get exam-ready with focused practice on AP Statistics Unit 7: Inference for Quantitative Data: Means. Strengthen your understanding through realistic questions, clear explanations, and detailed feedback with UWorld’s AP Stats Unit 7 review, your key to scoring higher and feeling confident on test day.

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Engaging Video Lessons

Understand tricky AP Stats concepts such as inference procedures and hypothesis testing through simple, engaging video lessons. These sessions explain key topics from the AP Statistics Unit 7 progress check MCQ and link them to real AP exam questions, making complex ideas easier to grasp and apply.

Read

Interactive Study Guides

Review essential formulas and test strategies with detailed explanations in our Unit 7 AP Stats review guide. Each section aligns with AP Stat unit 7 review concepts, helping you connect theory to practice and prepare effectively for progress checks and the AP exam.

Practice

Sharpen Your Skills with AP Statistics Unit 7 Practice Sets

Test your understanding with AP Stats Unit 7 Progress Check MCQ-style questions. Practice applying inference concepts, analyzing data, and interpreting results to become exam-ready with real AP-style problems.
Try these sample practice questions with detailed answer explanations:
Inference for Quantitative Data: Means Practice Tests

Question

Which of the following statements is true about the t-distribution?

  1. It is symmetric.
  2. It is more spread out than the standard normal distribution.
  3. As the degrees of freedom get smaller, its dispersion gets smaller.
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Hint:

The t-distribution is a continuous probability distribution similar to the standard normal distribution. Its spread depends on the degrees of freedom, which is defined differently for different hypothesis tests.

Explanation

A t-distribution is a continuous probability distribution that is similar in many aspects to the standard normal distribution: bell-shaped and symmetric. Statement I is true.

The spread of the t-distribution depends on the degrees of freedom (df), the value of which is defined differently for different hypothesis tests.

An increase in df makes the t-distribution less spread out and closer to the standard normal distribution. A decrease in df makes the t-distribution more spread out and farther from the standard normal distribution.

The t-distribution is always more spread out than the normal distribution, and its dispersion gets larger (not smaller) as the degrees of freedom get smaller. Statement II is true, but Statement III is false.

Therefore, of the given statements, only I and II are true.

Things to remember:
A t-distribution is a continuous probability distribution, and (similar to the standard normal distribution) it is bell-shaped and symmetric. The spread of the t-distribution depends on the degrees of freedom (df):

  • An increase in df makes the t-distribution less spread out and closer to the normal distribution.

  • A decrease in df makes the t-distribution more spread out and farther from the normal distribution.

Question

A doctor conducted a small study to investigate fasting blood sugar levels in adult patients with diabetes. A random sample of 20 people was selected from the names of all his patients who have diabetes. Of the people in the sample, the mean fasting blood sugar level was 182.23 milligrams per deciliter (mg/dL) with a standard deviation 12.67 mg/dL. The doctor decided to construct a 90 percent confidence interval for the mean fasting blood sugar level, in mg/dL, of all his patients with diabetes. Assuming all conditions for inference are met, which of the following is closest to the critical value for the 90 percent confidence interval?

A. 1.282
B. 1.327
C. 1.645
D.1.729
E. 1.960

Hint:

A critical value is a boundary used to identify the middle C% of a probability distribution, where C% is the confidence level of a confidence interval.

Explanation

A critical value is a boundary used to identify the middle C% of a probability distribution, where C% is the level of confidence of a confidence interval (CI). It is the multiplier that makes a CI wide enough to have C% confidence level..

The doctor will construct a CI for a population mean μ (mean fasting blood glucose level of all his patients with diabetes). The critical value for a CI for μ depends on the method used to construct the CI.

No information is given about the population, so assume that the population SD is unknown. The proper method to construct the CI is a t-interval, and the critical value is a t-score (t*).

The critical value t* of a 90% CI for μ is the t-score that captures the central 90% (and accumulates 95%) of the area under the t-distribution with degrees of freedom (df) equal to the sample size n minus one: n − 1.

It is given that a random sample of 20 people was selected, so the critical value t* is the t-score that accumulates 95% of the area under the t-distribution with 20 − 1 = 19 df. The notation for the critical value t* is t19, 0.95.

To find t19, 0.95, first locate the inverse t-distribution (invt) function on a calculator. Input the area under the curve for a 90% CI (cumulative area = 0.95) and df = 19.

The answer choice that is closest to the critical value for the 90% CI for the mean fasting blood glucose level of all the doctor's patients with diabetes is t* = 1.729.

Note: It is possible to determine the critical t-score (t*) using a t-distribution table (see table).

(Choice A) This choice results from the error described in Choice C and from mistakenly determining the critical value for an 80% CI (1.282).

(Choice B) This choice results from mistakenly determining the critical value for an 80% CI (t19, 0.90 = 1.327) instead of the critical value for a 90% CI (t19, 0.95 = 1.729).

(Choice C) This choice results from mistakenly finding the critical value for a z-interval (based on the standard normal distribution), but the appropriate interval is a t-interval because the population SD is unknown.

(Choice E) This choice results from the error described in Choice C and from mistakenly determining the critical value for a 95% CI (1.960).

Things to remember:

  • Use a t-interval to construct a confidence interval (CI) for a mean μ when the conditions for inference are met and standard deviation (SD) of the population is unknown.
  • The critical value t* for a C% CI for μ is the t-score that captures the central C% of the area under the t-distribution with degrees of freedom (df) equal to n − 1.

Question

Jane and Ryan are best friends. They live in different cities and take a train whenever they visit each other. Jane believes that it takes her longer to get to Ryan than it does for Ryan to get to her. Jane and Ryan decided to collect data to see if her train transit time is longer than his. They recorded the transit time in hours. After convincing themselves that the assumptions were reasonable, they conducted a two-sample t-test and obtained the following results.

Two-sample T for Jane's transit time vs Ryan's transit time
N Mean StDev SE Mean
Jane's transit time 15 2.31 0.96 0.25
Ryan's transit time 15 2.04 0.71 0.18
90% CI for μ1 Jane's transit time − μ2 Ryan's transit time: (−0.256, 0.796)
T-Test: μ1 Jane's transit time = μ2 Ryan's transit time (vs >): T = 0.876, P = 0.194, DF = 25.8

Using a significance level of 0.10, which of the following statements best describes the conclusion that can be drawn from these data?

A. There is convincing evidence that the mean transit time for Jane is greater than the mean transit time for Ryan.
B. There is not convincing evidence that the mean transit time for Jane is greater than the mean transit time for Ryan.
C. There is convincing evidence to conclude that there is a difference in the mean transit time between Jane and Ryan.
D. There is not convincing evidence to conclude that there is a difference in the mean transit time between Jane and Ryan.
E. The t-test cannot be used for samples that are this small.

Hint:

Use the p-value to determine the statistical significance of the appropriate hypothesis test.

Explanation

To draw conclusions about the given data, first identify the null H0 and alternative Ha hypotheses. Then compare the p-value to the significance level α to determine if there is convincing evidence in favor of Ha.

It is given that a two-sample t-test was conducted to determine whether the mean transit time for Jane (µ1) is greater than the mean transit time for Ryan (µ2), so H0 and Ha are the following:

If p-value ≤ α, there is convincing evidence that Ha is true (mean transit time is greater for Jane than for Ryan).
If p-value > α, there is not convincing evidence that Ha is true (mean transit time is not greater for Jane than for Ryan).

Notice that the given p-value is greater than the significance level α (0.194 > 0.10), so there is not convincing evidence in favor of Ha.

Therefore, the most appropriate conclusion that can be drawn from the data is:

There is not convincing evidence that the mean transit time for Jane is greater than the mean transit time for Ryan.

(Choice A) The p-value is greater than the significance level α, so there is not convincing statistical evidence in favor of Ha.

(Choices C and D) These choices describe conclusions based on a two-sided hypothesis test, which evaluates if there is a difference between two means. However, the question asks for a one-sided test, which evaluates if one mean is greater than another.

(Choice E) The sample size is sufficient to conduct the test because the question states that the assumptions were reasonable to conduct the test.

Things to remember:
To determine whether there is convincing statistical evidence against a null hypothesis H0 and in favor of an alternative hypothesis Ha, compare the p-value to the significance level α.

  • If p-value ≤ α, there is convincing evidence in favor of Ha.
  • If p-value > α, there is not convincing evidence in favor of Ha.
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Frequently Asked Questions (FAQs)

AP Statistics Unit 7 dives deep into inference for quantitative data, teaching you how to analyze sample data, test claims, and estimate population means with precision. This unit builds the foundation for interpreting real-world results and applying statistical reasoning confidently in any scenario.

  • Constructing and interpreting a confidence interval for a population mean: Learn to estimate a population mean using sample data and interpret the range of plausible values accurately in AP Statistics Unit 7.
  • Setting up and carrying out a test for a population mean: Discover how to form hypotheses, calculate test statistics, and determine significance—skills reinforced in AP Stats unit 7 progress check MCQ.
  • Interpreting a p-value and justifying a claim about a population mean: Understand how to evaluate evidence and justify conclusions, a common focus in AP Stats unit 7 FRQ practice.
  • Confidence intervals and tests for the difference of two population means: Compare two groups’ means to determine statistical differences, a key concept explored in AP Stats Unit 7 review exercises.

Build confidence through UWorld’s AP Stats unit 7 practice test, where expert-written questions and clear explanations mirror real AP exam scenarios, helping you master every inference concept before test day.

The best way to prepare for AP Statistics Unit 7 is to follow the Read–Watch–Practice method—an effective approach for mastering inference topics like confidence intervals and hypothesis tests.

  • Read: Start by reviewing your notes and study guides that explain AP Stats inference procedures and concepts from AP Statistics Unit 7 progress. Check MCQs on definitions, formulas, and when to use one-sample vs. two-sample t-tests.
  • Watch: Reinforce what you’ve read by watching detailed lesson videos or walkthroughs for AP Stats Unit 7 progress check MCQ. Seeing problems solved step-by-step helps connect concepts to real-world applications.
  • Practice: Apply your knowledge through unit 7 AP Stats FRQ and AP Stats Unit 7 MCQ questions. Regular practice helps identify weak areas and build confidence.

Prepare efficiently with UWorld’s interactive explanations and performance tracking tools—they make it easy to review, practice, and retain every concept from Unit 7.

If you’re preparing for AP Statistics Unit 7: Inference for Quantitative Data—Means, there are several high-quality free resources to help you review core concepts and practice effectively before test day.

  • College Board: Access the official AP Stats Unit 7 progress check MCQ and Unit 7 AP Stats FRQ practice sets through AP Classroom. These questions mirror the real AP exam and give you a clear picture of what to expect.
  • Khan Academy: Offers comprehensive, free video lessons and exercises on AP stats inference procedures, confidence intervals, and hypothesis testing. It’s a great way to strengthen your conceptual foundation.
  • UWorld: With UWorld’s free trial, you can explore expertly written AP Statistics Unit 7 review questions and detailed explanations that go beyond memorization—helping you understand why each answer is correct.

Start your prep with free resources, but level up with UWorld’s realistic AP-style questions and powerful learning tools. It’s everything you need to transform understanding into high-scoring performance.

The AP Statistics Unit 7 test includes both Multiple-Choice Questions (MCQs) and Free-Response Questions (FRQs) that focus on inference for quantitative data. You’ll apply statistical reasoning to real-world contexts, interpret results, and justify conclusions using proper notation and reasoning.

  • MCQs: Expect questions similar to AP Stats Unit 7 Progress Check MCQ and AP Stats Unit 7 Progress Check MCQs, which test concepts like confidence intervals, hypothesis testing, and interpreting p-values.
  • FRQs: These questions, modeled after the unit 7 AP Stats FRQ, require showing your work—calculating test statistics, checking conditions, and explaining results clearly.

To prepare, combine official College Board practice with UWorld’s AP Statistics Unit 7 review sets. UWorld’s detailed explanations and step-by-step solutions help you build accuracy, speed, and confidence for both MCQs and FRQs.

To score higher on AP Statistics Unit 7 FRQs, focus on clarity, structure, and correct interpretation of results. FRQs test how well you can apply inference procedures to real-world scenarios, so your reasoning matters as much as your calculations.

  • Understand the process: Review examples from unit 7 AP Stats FRQ and the AP Statistics unit 7 progress check FRQ to see how each response should include hypotheses, conditions, calculations, and conclusions in context.
  • Show all steps: Clearly write formulas, plug in values, and interpret confidence intervals or p-values.
  • Practice under time limits: Use AP Stats Unit 7 Progress Check MCQ and FRQ-style questions to simulate exam timing and improve accuracy.

UWorld’s AP Stats Unit 7 review offers guided solutions and modeled FRQ responses that teach you how to think like an AP scorer, helping you earn every possible point.

To boost your performance on AP Statistics Unit 7 MCQs, focus on mastering key concepts, identifying patterns in questions, and practicing consistently. The MCQs often test inference concepts, assumptions, and interpretation of results rather than memorization.

  • Review important topics: Revisit AP Stats inference procedures and concepts from AP Stats Unit 7 progress check MCQ, including confidence intervals, t-tests, and p-values.
  • Analyze question patterns: Practice with AP Stats Unit 7 MCQ-style problems to learn how small changes in data or context affect the correct answer.
  • Practice strategically: Use timed quizzes to improve speed and accuracy. Review both correct and incorrect answers to understand reasoning.

UWorld’s AP Statistics unit 7 review gives you exam-style MCQs with detailed, visual explanations, helping you strengthen conceptual understanding and build confidence for the real test.

AP Statistics Unit 7: Inference for Quantitative Data, Means typically make up 10–18% of the total AP Statistics exam. This means it’s one of the most important units to master, as it directly tests your ability to perform t-tests, interpret p-values, and construct confidence intervals for population means.

You’ll see these topics appear in both the AP Stats Unit 7 progress check MCQ and Unit 7 AP Stats FRQ, often requiring you to justify conclusions or interpret data in context. Questions may also connect Unit 7 with earlier topics, like sampling and variability, to test a deeper understanding.

To maximize your understanding of this high-weight unit, practice using UWorld’s AP Statistics Unit 7 review questions. They mirror real exam difficulty and provide clear, step-by-step explanations, ensuring you’re confident when these key inference topics appear on test day.

To ace AP Statistics Unit 7 on quantitative data, you need a solid study guide to help you learn about confidence intervals, hypothesis testing, and inference methods. The guide needs to explain not only how to do these statistical calculations but also why they work. Additionally, it should have lots of practice problems.

Start with the College Board’s AP Statistics Course and Exam Description, which outlines what Unit 7 covers and provides sample multiple-choice and free-response questions. This is your best reference for official exam expectations. Khan Academy is another great free option, it offers short, focused video lessons and interactive quizzes on topics like constructing and interpreting confidence intervals and conducting t-tests. These resources are perfect for reinforcing classroom learning at your own pace.

However, if you want a complete, exam-level prep experience, UWorld’s AP Statistics study resources go beyond basic guides. Each topic, like the difference of two population means or interpreting p-values, is paired with expertly written questions that mirror real AP exam difficulty. Every question includes a step-by-step explanation, visual data representations, and reasoning tips to help you think like an AP grader. You can also track progress, identify weak areas, and build confidence through repeated practice.

Start with UWorld’s free trial to explore Unit 7 study materials, then upgrade for full access to all topics, question types, and analytics. With its structured approach and detailed guidance, UWorld is one of the most effective ways to prepare for the AP Statistics Unit 7 test and boost your overall exam score.

Yes! You can find AP Statistics Unit 7 practice tests from several trusted sources that target topics like inference for means, confidence intervals, and hypothesis testing. These focused practice sets are great for checking how well you understand Unit 7 before moving on to full-length exams.

Here’s where you can find reliable Unit 7-specific practice materials:

  • College Board AP Classroom: Offers official Unit 7 progress checks (MCQ and FRQ) that reflect real exam style and difficulty. You will find AP Stats Unit 7 progress check multiple-choice questions (MCQs) that cover topics such as confidence intervals and inference procedures.
  • Khan Academy: Provides free quizzes and exercises aligned with the AP Statistics curriculum. You can practice question sets on constructing and interpreting confidence intervals and testing population means with instant feedback.
  • UWorld AP Statistics Practice Tests: UWorld offers exam-style Unit 7 practice questions that replicate the tone and complexity of real AP questions. Each question includes detailed explanations, data visuals, and reasoning steps to help you master both MCQ and FRQ problem-solving strategies. You can also track progress across topics to strengthen weaker areas.

For the best results, combine all three: start with College Board for familiarity, use Khan Academy for free practice, and rely on UWorld to simulate real testing conditions. Try UWorld’s free trial today to experience its detailed explanations and analytics firsthand, it’s one of the best tools to boost your Unit 7 confidence and overall AP Statistics score.

Before taking your AP Statistics Unit 7 test, it’s essential to follow a clear checklist to make sure you’re confident and prepared. Since Unit 7 focuses on Inference for Quantitative Data: Means, reviewing concepts, formulas, and practice questions in a structured way can help you perform your best.

Here’s your complete review checklist:

  • Review Key Concepts: Go through topics like constructing and interpreting confidence intervals, setting up hypothesis tests for population means, and interpreting p-values. Make sure you understand when to use one-sample and two-sample t-tests.
  • Practice MCQs and FRQs: Complete the AP Stats Unit 7 progress check MCQ on College Board’s AP Classroom to test your understanding. Use UWorld’s Unit 7 question bank for in-depth explanations and extra practice that closely aligns with the AP exam format.
  • Use Study Guides and Notes: Summarize critical formulas, inference conditions, and step-by-step problem-solving methods into a concise Unit 7 cheat sheet. Reinforce your understanding using Khan Academy and College Board’s topic breakdowns.
  • Simulate Exam Conditions: Take timed practice sessions using UWorld’s timed quiz mode to get used to real testing conditions and improve pacing.
  • Analyze Mistakes: Review every question you miss carefully. UWorld’s detailed answer explanations will help you understand your errors and avoid them on the actual exam.

Pro Tip: Track your performance with UWorld’s analytics tools to see your strengths and weak areas. With realistic questions, visual explanations, and interactive practice, UWorld gives you the edge you need to ace AP Statistics Unit 7.

AP Statistics Unit 7 can feel more challenging than earlier units because it moves beyond data description and introduces inference for means; a core skill in statistical reasoning. This unit expects you to apply formulas, interpret p-values, and construct confidence intervals while justifying conclusions in context. Unlike simpler topics such as data representation or probability, inference questions require both computation and interpretation, which is where many students struggle.

The key to mastering this unit is practice with realistic questions that mirror AP exam difficulty. UWorld’s AP Statistics Unit 7 review provides guided explanations for each inference procedure, helping you understand when to use one-sample versus two-sample tests, how to check conditions, and how to interpret your results clearly. With step-by-step feedback and data-driven insights, you’ll gain the confidence to tackle Unit 7 and related inference questions throughout the AP exam.

In AP Statistics Unit 7, students often lose points because of small but costly errors, such as forgetting to verify conditions, confusing standard deviation with standard error, or misinterpreting the meaning of a p-value. Another frequent mistake is not stating hypotheses clearly or failing to connect statistical results to real-world context. These issues can lower scores even when calculations are correct.

To avoid these common pitfalls, practice with guided, exam-style questions that highlight each step of the inference process. UWorld’s AP Stats Unit 7 practice test walks you through every stage, from setting up hypotheses and calculating test statistics to interpreting results accurately. Each explanation identifies where students often go wrong and reinforces the correct reasoning, so you can approach every inference question with precision and confidence.

Preparing for AP Statistics Unit 7 requires both conceptual understanding and consistent practice. Begin by reviewing your class notes on inference for quantitative data, focusing on how confidence intervals and hypothesis testing connect to sampling variability. Then, reinforce those ideas by solving multiple-choice and free-response questions that require applying these concepts to real-world data. Time yourself occasionally to build exam endurance and accuracy under pressure.

For a more structured approach, use UWorld’s AP Statistics Unit 7 review, which organizes your prep into lessons, video walkthroughs, and exam-style practice sets. Each question includes an in-depth explanation and visual aid to help you grasp difficult inference ideas easily. With its performance tracking and progress dashboard, UWorld helps you identify weak areas, refine your approach, and feel fully prepared for both the Unit 7 test and the full AP Statistics exam.

Mastering Unit 7 gives you a major advantage on the AP Statistics exam because it lays the groundwork for all later inference topics. The logic behind confidence intervals, p-values, and t-tests connects directly to future units and shows up across both multiple-choice and free-response questions. When you understand these procedures thoroughly, you can justify your reasoning clearly, something AP graders consistently reward.

Here’s how mastering Unit 7 supports your overall exam performance:

  • Builds exam readiness: Core inference skills appear throughout the test, so mastering them boosts your performance in multiple sections.
  • Strengthens conceptual understanding: Knowing when and how to use t-procedures helps you approach complex data questions with confidence.
  • Improves communication: Writing clear conclusions using correct statistical language earns you higher FRQ scores.
  • Connects key ideas: Unit 7 links earlier topics like sampling and variability to inference concepts, reinforcing your overall understanding.

UWorld’s AP Statistics Unit 7 practice questions go beyond simple recall—they train you to apply inference reasoning in realistic, AP-style scenarios. Each problem mirrors the tone and difficulty of the real exam, with visual explanations and step-by-step breakdowns for every answer choice. By practicing with UWorld, you’ll not only master Unit 7 but also build the analytical and writing skills needed to excel on the entire AP Statistics exam.

Interpreting p-values and confidence intervals accurately is one of the most essential skills in AP Statistics Unit 7. The p-value tells you how strong the evidence is against the null hypothesis, while the confidence interval shows a plausible range of values for a population mean. Students often mix up these ideas, thinking a p-value gives the probability that the null is true, or that a confidence interval contains the true mean with certainty. Learning how to interpret them correctly is key to writing precise, high-scoring responses on both MCQs and FRQs.

To strengthen your understanding, practice questions that require you to connect statistical results to real-world conclusions. UWorld’s AP Stats Unit 7 review includes detailed explanations, visual data summaries, and sample interpretations for every inference concept. By practicing these scenarios, you’ll not only master p-values and confidence intervals but also build the reasoning skills needed to explain your conclusions clearly and confidently on the AP exam.

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Upon a successful transaction, you will be sent a confirmation email receipt.

A renewal is an extension of time to continue accessing an active subscription, and it will not start the subscription over, provide a reset, or grant access to additional questions that were not previously accessible. Because a renewal is an extension to an already active subscription, it is effective from the existing expiration date, not from the date of purchase, and cannot be deferred in any way to start at a later date/time.

Please note that to qualify for renewal pricing, you will need to renew the course before it expires. Renewals are not offered to expired subscriptions. If you fail to secure a renewal before the expiration date, you will need to purchase a new subscription at the regular price directly from our website to regain access to the material.

Note: All times and dates displayed for subscription expiration correspond with the Eastern Time Zone (GMT/UTC -5 hours or New York Time), which may be different than your local time zone.

Note: If your initial purchase was a combination package, you will need to renew each active subscription individually. You do not need to renew a course that has not been activated.

You may request to upgrade or downgrade your subscription purchase as long as it has not been activated. If you purchase a combination package, all included subscriptions must be unused. Please be advised that current subscription pricing will apply.

If your subscription has been activated, unfortunately, we cannot upgrade it retroactively. If seeking to downgrade, please refer to our refund policy for available options.

We do not offer custom duration(s) or combination packages other than those outlined on the website. Please refer to our purchase page for currently available subscriptions (including discounted combination packages for some products).

Self-Assessment exam subscriptions are for 14 days each. Subscribers whose active subscription(s) have not expired can purchase renewals from 7 days or more at any time before their active subscription expires. Please refer to the respective course description page for renewal options.

We offer a demo on each of our product pages that contains a sample of the product interface and a few sample questions. We do not offer guest/trial accounts to test our software and view materials.

It is possible to purchase a subscription as a gift for someone else. However, the intended recipient will need to register an account on our website (or have an account registered for them, with their profile information entered accurately). If the user is present at the time of purchase, the purchase can be made from their account on our website using any credit or debit card with a Visa, MasterCard, American Express, or Discover logo.

If the user is not present, or you wish for the gift to be a surprise, please contact Support directly using the contact form to arrange payment for the gift subscription. You will need to provide the user’s registered email address so the account can be located.