Question 3: Inference
Laptop versus phone typing (paired t-test)
- Units 1 and 4
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A complete hypothesis test or confidence interval: you identify the variables, name the procedure, state hypotheses and parameters, check the conditions, do the calculations, and justify a conclusion in context. It uses the inference skills from Practices 2, 3 and 4. On the exam: Question 3 of 4 (official name: Inference (Hypothesis Test or Confidence Interval)). 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 D, and label any subparts (for example, i and ii).
The typing comparison
A technology teacher wondered whether students type faster on a laptop keyboard than on a phone. She randomly selected 12 of the 640 students in her school's 11th grade. Each selected student took the same 2-minute typing test on a laptop and on a phone, in an order decided by a coin flip. The typing speeds, in words per minute (wpm), are in the table.
At the α = 0.05 significance level, complete the appropriate inference procedure to determine whether there is convincing statistical evidence that the mean typing speed of all 11th graders at the school is greater on a laptop than on a phone.
Source: Hypothetical scenario
Typing speed (words per minute)
| Student | Laptop | Phone |
|---|---|---|
| 1 | 62 | 58 |
| 2 | 55 | 57 |
| 3 | 71 | 64 |
| 4 | 48 | 46 |
| 5 | 66 | 59 |
| 6 | 59 | 60 |
| 7 | 74 | 66 |
| 8 | 52 | 50 |
| 9 | 68 | 61 |
| 10 | 57 | 49 |
| 11 | 63 | 63 |
| 12 | 70 | 62 |
Source: Hypothetical data
Suggested time: 22 minutes
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Part (A)
2 pointsIdentify and classify the variables in the study.
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Part (B)
1 pointIdentify the appropriate inference procedure.
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Part (C)
5 pointsComplete the inference procedure. Include the hypotheses, a definition of the parameter, a check of the conditions, and the test statistic and p-value.
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Part (D)
2 pointsJustify a conclusion in context.
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