DP Math AI · HL · Statistics and Probability

AHL 4.12—Data collection, reliability and validity tests

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  1. Question 1

    A researcher categorises exam scores into 8 groups and tests whether they follow a Poisson distribution, estimating the parameter λ from the sample data. What is the correct number of degrees of freedom for the chi-squared goodness of fit test?
    No clue? Show me the answer
    Correct answerCorrect!Incorrect
    A6

    Step-by-step walkthrough

    Choose a solution method

    Method #1Worked solution

    Step 1: State the formula

    df=categories−1−parameters estimated.

    Step 2: Substitute values

    There are 8 categories and 1 parameter (λ) estimated from the data.

    Step 3: Compute df

    df=8−1−1=6.

    Step 4: Conclusion

    The correct degrees of freedom is 6.

    Method #2Why the others are wrong

    Step 1: Option B

    7 comes from forgetting to subtract the estimated parameter λ, only applying the −1 for total probability.

    Step 2: Option C

    5 results from mistakenly subtracting 2 parameters, as if fitting a normal distribution instead of a Poisson.

    Step 3: Option D

    8 ignores both the −1 constraint and the parameter subtraction entirely.

    Step 4: Correct choice

    Only df=6 correctly applies both subtractions.

  2. Question 2

    Which of the following survey questions is an example of a double-barrelled question?
    No clue? Show me the answer
    Correct answerCorrect!Incorrect
    B"Do you find the new app easy to use and reliable?"

    Step-by-step walkthrough

    Choose a solution method

    Method #1Worked solution

    Step 1: Define double-barrelled

    A double-barrelled question asks about two separate attributes within a single question.

    Step 2: Examine option A

    "Easy to use" and "reliable" are two distinct attributes bundled into one question.

    Step 3: Check for ambiguity

    A respondent finding the app easy but unreliable cannot answer honestly with one response.

    Step 4: Conclusion

    Option A is the double-barrelled question.

    Method #2Why the others are wrong

    Step 1: Option B

    This asks about a single attribute (ease of use) using a defined scale - well constructed.

    Step 2: Option C

    This asks about a single behaviour (frequency of use) with no ambiguity.

    Step 3: Option D

    This is a leading question, not double-barrelled - it pushes toward a positive answer but only addresses one concept (quality/value combined loosely, but the defining flaw here is bias, not two separate measurable constructs).

    Step 4: Correct choice

    Only option A explicitly combines two separate measurable constructs.

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14 more questions in this topic

← Previous topicSL 4.11—Expected, observed, hypotheses, chi squared, gof, t-testNext topic →AHL 4.13—Non-linear regression
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