These are original Marlbridge practice questions, not past exam questions. All studies, places and data are fictional. The rubrics are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. Assumptions for every question: “randomly selected” or “randomly assigned” means a random mechanism, such as a random number generator, was used; round percentages to 1 decimal place.
Question 1 (multiple choice · foundation)
Which of these studies is a census?
- (A) A city council phones 400 randomly chosen adult residents to ask about recycling.
- (B) A teacher records the height of every one of the 28 students in her class to describe that class.
- (C) A factory tests 50 of the 2,000 batteries it made on Monday to check their lifetimes.
- (D) A news website posts a poll, and 3,000 visitors choose to answer it.
Answer and explanation
Answer: (B). The population is the teacher’s class of 28 students, and she records the height of every one of them. A census records information from every individual in the population.
- (A) records only 400 of the city’s adults. A random sample is still a sample, not a census.
- (C) tests 50 of 2,000 batteries. Testing every battery would destroy them all, which is one reason to sample.
- (D) records only the visitors who chose to answer. A large number of responses does not make it a census; most of the site’s readers are missing.
Question 2 (multiple choice · core)
A gardener has 24 tomato plants. Each plant is given one of three fertilisers (A, B or C) and is watered either daily or every other day. The combinations are assigned to plants at random, with the same number of plants for each. After six weeks, the height of each plant is measured.
How many treatments are there in this experiment?
- (A) 2
- (B) 5
- (C) 6
- (D) 24
Answer and explanation
Answer: (C). There are two factors: fertiliser (3 levels) and watering schedule (2 levels). Each combination of levels is a treatment, so there are 3 × 2 = 6 treatments, for example “fertiliser B, watered every other day”. Each treatment is given to 24 ÷ 6 = 4 plants.
- (A) counts the factors, not the treatments.
- (B) adds the levels (3 + 2). With more than one factor, the levels must be combined, so you multiply.
- (D) counts the experimental units (the plants), which receive the treatments.
Question 3 (multiple choice · core)
A fitness app asks its users to take part in a study. 900 users volunteer. A random number generator assigns each volunteer to receive either a daily reminder to exercise or no reminder. After eight weeks, the mean weekly exercise time is clearly higher in the reminder group. Which conclusion is most appropriate?
- (A) Reminders cause more exercise for all users of the app, because 900 is a large sample.
- (B) Reminders cause more exercise for users like those who volunteered.
- (C) Reminders are associated with more exercise, but cause and effect cannot be concluded because volunteers were used.
- (D) No conclusion can be drawn, because the users were not randomly selected.
Answer and explanation
Answer: (B). Treatments were randomly assigned, so a cause-and-effect conclusion is possible. The units were volunteers, not a random sample of all users, so the conclusion applies only to users similar to the volunteers.
- (A) generalises to all users. Sample size does not make volunteers a random sample.
- (C) mixes up the two ideas. Volunteers limit who you can generalise to; random assignment is what allows cause and effect.
- (D) goes too far. A study without random selection still supports conclusions about individuals like those studied.
Question 4 (classification · core)
For each study, state whether it is an experiment or an observational study. If it is observational, say whether it is prospective, retrospective or a survey. Give a reason each time.
(a) A researcher selects 120 cafés that opened in a region this year. She records whether each has outdoor seating, then records its monthly sales for the next three years. (b) A sports club gives all 40 of its junior members the same questionnaire about weekly training hours and hours of sleep. (c) An engineer selects 60 road bridges today and looks up their maintenance records for the past 20 years. (d) A teacher uses a random number generator to give 15 of her 30 students printed revision notes and the other 15 digital notes, then compares their test scores.
Worked solution and suggested Marlbridge rubric
(a) Observational, prospective. Nothing is imposed: outdoor seating is recorded, not assigned. The cafés are chosen now and followed forward in time.
(b) Observational, survey. Data come from people answering a standard set of questions, and no treatment is imposed. (It is also a census of the junior members, since all 40 are asked.)
(c) Observational, retrospective. The bridges are chosen now and past records are gathered. The engineer imposes nothing.
(d) Experiment. The teacher assigns the type of notes (the treatment) to each student, then measures the response (test score).
| Point | What earns it |
|---|---|
| 1 | (a) observational and prospective, with a reason about recording forward in time |
| 1 | (b) observational survey, with a reason about standard questions to people |
| 1 | (c) observational and retrospective, with a reason about past data |
| 1 | (d) experiment, with a reason that the teacher assigned the treatments |
A classification with no reason does not earn the point.
Question 5 (constructed response · core)
At the fictional Calder University, 45 students volunteer for a memory study. A random number generator assigns 15 students to each of three conditions: learning a list of 30 words in silence, with quiet background chatter, or with loud background chatter. Each student then writes down as many of the words as they can remember.
(a) Explain why this is an experiment. (b) Identify the experimental units, the factor and its levels, the treatments, and the response variable. (c) The silence group remembers the most words on average, and the difference is large. What can the researcher conclude, and about whom? (d) A colleague wants to repeat the study using two kinds of list (words or numbers) as a second factor. How many treatments would the new study have?
Worked solution and suggested Marlbridge rubric
(a) The researcher assigns the noise condition to each student, then measures the outcome. Treatments are imposed, so it is an experiment.
(b) Experimental units: the 45 students (also called subjects or participants). Factor: background noise, with 3 levels (silence, quiet chatter, loud chatter). Treatments: the three levels, since there is only one factor. Response variable: the number of words (out of 30) each student remembers.
(c) Because conditions were randomly assigned, the researcher can conclude that background noise causes a change in the number of words remembered. Because the students volunteered, the conclusion applies only to students like these volunteers, not to all students or all adults.
(d) 3 noise levels × 2 list types = 6 treatments.
| Point | What earns it |
|---|---|
| 1 | (a) Says the treatments (noise conditions) are imposed or assigned by the researcher |
| 1 | (b) Correct units, factor with all three levels, treatments (the three levels), and response variable with what is counted |
| 1 | (c) Cause and effect justified by random assignment and scope limited to students like the volunteers |
| 1 | (d) 6 treatments, with the multiplication shown |
In (c), an answer that generalises to all students does not earn the point, even if the causal part is correct.
Question 6 (constructed response · stretch)
Marsh Lane College (fictional) has 1,500 students. A random number generator selects 200 of them. Each selected student is asked whether they used a particular revision app this term, and the college records whether they passed the end-of-term test.
| Passed | Did not pass | Total | |
|---|---|---|---|
| Used the app | 62 | 18 | 80 |
| Did not use the app | 66 | 54 | 120 |
| Total | 128 | 72 | 200 |
(a) Is this an observational study or an experiment? Explain. (b) Calculate the pass rate for each group. (c) A local newspaper reports: “Revision app raises pass rates.” Explain why this conclusion is not justified. In your answer, describe a possible confounding variable and how it is linked to both variables. (d) To which students can the results be generalised? Explain. (e) Write an investigative question for this study, with all three components, that asks for a test of whether app users have a higher pass rate.
Worked solution and suggested Marlbridge rubric
(a) Observational study. Students chose for themselves whether to use the app; the college did not assign it. Data were only recorded.
(b) App users: 62 ÷ 80 = 77.5%. Non-users: 66 ÷ 120 = 55.0%. App users passed at a rate 22.5 percentage points higher in this sample.
(c) In an observational study, another variable may explain the difference. A possible confounding variable is how motivated a student is to revise. More motivated students are more likely to download and use a revision app (link to the explanatory variable). More motivated students also tend to revise more in other ways, so they are more likely to pass (link to the response). The higher pass rate could be due to motivation, not the app, so “raises” (a causal claim) is not justified.
(d) The 200 students were randomly selected from all 1,500, so the results can be generalised to all students at Marsh Lane College. They cannot be generalised to students at other colleges.
(e) One acceptable answer: “Among all Marsh Lane College students this term, is the proportion who passed the end-of-term test greater for students who used the revision app than for students who did not?”
- Data: app use (yes/no) and test result (passed/did not pass).
- Analysis: test about the difference between two population proportions, direction “greater than”.
- Conclusion: about all Marsh Lane College students; association only, not cause.
| Point | What earns it |
|---|---|
| 1 | (a) Observational, because app use was chosen by students, not assigned; and (b) both pass rates correct |
| 1 | (c) Names a plausible confounding variable and links it to both app use and passing, in context |
| 1 | (d) All Marsh Lane College students, justified by random selection |
| 1 | (e) Question names the variables, the parameter (proportions passing) with the direction “greater”, and the population |
Other confounders (for example, how much time a student has for revision) earn the point in (c) only if both links are explained. A question in (e) that asks “how large is the difference” earns the point only if it also states a direction for a test.
Question 7 (explanation · stretch)
The secretary of a cycling club with 520 members wants to know whether members think the Sunday ride is too long. She first writes the investigative question: “Is the Sunday ride OK?”
(a) Explain why this is not a full investigative question. (b) Rewrite it as an investigative question that asks for an estimate, with all three components. (c) The secretary emails all 520 members, and 80 of them reply. She says: “I emailed everyone, so this is a census.” Is she right? To whom can the results be generalised? Explain.
Model answer and suggested Marlbridge rubric
(a) “OK” is vague. The question does not say what variable to record, what to calculate, or who the conclusion is about.
(b) “What proportion of the club’s 520 members think the Sunday ride is too long? Give a range of plausible values for this proportion.”
- Data: each member’s answer to “Is the Sunday ride too long?” (yes/no).
- Analysis: estimate the population proportion with a range of plausible values.
- Conclusion: about the club’s members.
(c) No. A census records information from every member, but only 80 of the 520 (15.4%) replied. The 80 chose to reply, so they are volunteers, not a random sample. The results can be generalised only to members like those who replied. Members with strong views about the ride may be more likely to reply, so they may not represent the whole club.
| Point | What earns it |
|---|---|
| 1 | (a) Identifies that the variable, the analysis or the population is missing or vague |
| 1 | (b) Names the variable, the parameter (proportion of members) with estimation as the goal, and the population |
| 1 | (c) Not a census, because only 80 replied and results apply only to members like the volunteers |
How did you do?
- Q1 or Q7(c) wrong: re-read “Who is measured? Census or sample” in the study guide.
- Q2 or Q5 wrong: revisit “Experiments” and Worked example 1. Multiply the levels to count treatments.
- Q3, Q5(c) or Q6(d) wrong: revisit “Who can the conclusions be about?” and Figure 2.
- Q4 wrong: revisit “Observational studies” and Figure 1.
- Q6(c) wrong: revisit “Confounding variables”. Always show both links.
- Q6(e) or Q7(b) wrong: revisit “The three components of an investigative question” and Worked example 2.
Then tick off the topic checklist.