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  • Perplex
    IB Math AISL
    /
    Descriptive Statistics
    /

    Problem Bank

    [Maximum mark: 6]

    A bottled-water company claims that its 500 mL bottles contain on average 500 mL of water. To check this, a consumer independently purchases 25 bottles and measures the actual volume ​x​ (in mL) in each.


    She finds

    ​
    ∑x=12,450,∑x2=6,203,004
    ​
    1. Find an unbiased estimate of the true mean volume ​μ.

      [1]

      To earn a crown, get your answer ready before you reveal the options!

    2. Use the formula:

      ​
      s2=n−1∑x2−n(∑x)2​​
      ​

      to determine an unbiased estimate of the variance of the bottle volumes.

      [2]
    3. Construct a ​95%​ confidence interval for ​μ.

      [2]
    4. State in context a valid conclusion about the company’s claim at the ​5%​ significance level.

      [1]

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