Question 4: Multi-focus question
Testing a practice app by simulation
- Units 1, 2 and 3
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A multi-part question that pulls together several units, such as probability from a table, a summary statistic and an inference procedure, and asks you to calculate, interpret and justify a claim. It uses Practices 2, 3 and 4. On the exam: Question 4 of 4 (official name: Multi-Focus on Practices 2, 3, and 4). Section II has 4 free-response questions in 90 minutes (50% of the score); each question is worth 10 points and 12.5% of the score. The exam is fully digital in Bluebook, a graphing calculator with statistical capabilities is expected, and the formula sheet and tables are provided.
The question and its sources
Show the work that leads to each answer, and explain your reasoning in the context of the situation. A graphing calculator with statistical capabilities, the formula sheet and the statistical tables are available. Use the information given to answer parts A through I, and label any subparts (for example, i and ii).
The practice-app experiment
A math teacher wanted to know whether a new practice app helps students pass a unit test. Forty students in her classes volunteered. She randomly assigned 20 of them to use the app for two weeks and the other 20 to study as usual. On the unit test, 15 of the 20 app users passed and 9 of the 20 other students passed. The difference in pass rates (app − usual) was 0.75 − 0.45 = 0.30.
To see whether a difference this large could easily happen by chance alone, she assumed the app has no effect, so that the same 24 students would pass no matter which group they were in. A computer then randomly reassigned the 40 students' results to two groups of 20, 200 times, and recorded the difference in pass rates (app − usual) each time. The results are in the table.
Source: Hypothetical scenario
Simulated differences in pass rates (200 random reassignments)
| Simulated difference (app − usual) | Number of simulations |
|---|---|
| −0.4 | 2 |
| −0.3 | 8 |
| −0.2 | 30 |
| −0.1 | 50 |
| 0.0 | 46 |
| 0.1 | 34 |
| 0.2 | 19 |
| 0.3 | 8 |
| 0.4 | 3 |
Source: Hypothetical simulation results
Suggested time: 22 minutes
Your answers are saved in this browser as you type.
Part (A)
1 pointState the null and alternative hypotheses the teacher is testing.
0 / 2,500 characters
Part (B)
1 pointExplain what one value in the simulation represents.
0 / 2,500 characters
Part (C)
1 pointUse the simulation to estimate the p-value for the teacher's test. Show your work.
0 / 2,500 characters
Part (D)
2 points(i) At the α = 0.05 significance level, make a decision about the null hypothesis by comparing your p-value with α. (ii) State your conclusion in context.
0 / 2,500 characters
Part (E)
1 pointBased on your decision in part D, identify the type of error that could have been made, and describe it in context.
0 / 2,500 characters
Part (F)
1 pointSuppose the app really does increase the chance of passing. Explain how repeating the study with 80 volunteers (40 in each group) instead of 40 would affect the power of the test.
0 / 2,500 characters
Part (G)
1 pointExplain why a two-sample z-test for a difference in population proportions would not be appropriate for these data.
0 / 2,500 characters
Part (H)
1 pointOne of the 40 students who passed the test is selected at random. Calculate the probability that this student used the app.
0 / 2,500 characters
Part (I)
1 pointExplain to which students the results of this study can be applied.
0 / 2,500 characters
Checking scoring…
Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.