Estimators, standard error and bias

Estimators, standard error and bias Quiz

Spec 5.1 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Which estimator of μ\mu is unbiased, given that X1,X2,X3X_1,X_2,X_3 is a random sample with mean μ\mu?

    • A. X1+X2+X34\frac{X_1+X_2+X_3}{4}
    • B. X1+X2+X33\frac{X_1+X_2+X_3}{3}
    • C. X1+X2+X32\frac{X_1+X_2+X_3}{2}
    • D. X1+X2+X3X_1+X_2+X_3

  2. 2. A sample of size n=9n=9 has ∑(x−xˉ)2=72\sum(x-\bar x)^2=72. The unbiased estimate of σ2\sigma^2 is

    • A. 88
    • B. 99
    • C. 7.27.2
    • D. 7272

  3. 3. The estimator V=1n∑(Xi−Xˉ)2V=\frac1n\sum(X_i-\bar X)^2 of σ2\sigma^2 has bias

    • A. +σ2n+\frac{\sigma^2}{n}
    • B. 00
    • C. −σ2n-\frac{\sigma^2}{n}
    • D. −σ2n−1-\frac{\sigma^2}{n-1}

  4. 4. A sample of 1616 has s=6s=6. The estimated standard error of the sample mean is

    • A. 0.3750.375
    • B. 66
    • C. 99
    • D. 1.51.5

  5. 5. Two estimators of the same parameter are both unbiased, with variances σ24\frac{\sigma^2}{4} and σ22\frac{\sigma^2}{2}. Which is preferred?

    • A. The one with variance σ24\frac{\sigma^2}{4}, because it is more precise
    • B. The one with variance σ22\frac{\sigma^2}{2}, because it is larger
    • C. Neither, because both are unbiased
    • D. The one with variance σ22\frac{\sigma^2}{2}, because it uses fewer observations

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