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📊AP Statistics
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📊AP Statistics

FRQ 3 – Inference
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Unit 3: Inference for Categorical Data: Proportions
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AP Stats FRQ Types & Units

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

FRQFocusUnitsWhy
FRQ 1Multi-Focus on Practices 1 and 21Tests formulating an investigative question and collecting data (sampling, experimental design)
FRQ 2Multi-Focus on Practices 3 and 41, 2, 5Tests analyzing data and interpreting results — graphs, summary statistics, probability, regression output
FRQ 3Inference3, 4One complete inference procedure — a hypothesis test or confidence interval for proportions or means
FRQ 4Multi-Focus on Practices 2, 3, and 4AllCombines content areas across the course, assessing collecting, analyzing, and interpreting together

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 1 of 91/9

3. A smartwatch manufacturer is investigating whether a new firmware update reduces the occurrence of Bluetooth syncing failures. The engineering team selected a random sample of 500 smartwatches of a specific model. Half of the smartwatches (250) were randomly assigned to receive the new firmware, while the other half (250) remained on the standard firmware. Each smartwatch was then subjected to a week of automated syncing tests. The number of smartwatches that experienced at least one syncing failure during the week was recorded for each group.

The results are shown in Table 1. For the standard firmware, 38 of the 250 smartwatches experienced at least one syncing failure. For the new firmware, 18 of the 250 smartwatches experienced at least one syncing failure.

Firmware Type

Number of Smartwatches Tested

Number with at least one Syncing Failure

Standard

250

38

New

250

18

A.

State the appropriate null and alternative hypotheses for testing whether the proportion of all such smartwatches that would experience a syncing failure is lower for the new firmware than for the standard firmware. Define any parameters used.

B.

Identify the appropriate inference procedure and verify that the conditions for this procedure are met.

C.

Calculate the test statistic and the ppp-value for the procedure identified in Part B.

D.

Based on the ppp-value calculated in Part C, what conclusion should the engineering team make at the α=0.05\alpha = 0.05α=0.05 significance level?

E.

Describe a Type I error in the context of this study. Identify one potential consequence of making a Type I error for the smartwatch manufacturer.

Timed

00:00

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