QCEVault

Sampling and proportions — Question 142

Original QCE Vault practice · 1 mark

Q142 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 142

For a population proportion p=0.64p=0.64 and random samples of size 400400, which distribution best approximates the sampling distribution of p^\hat p?
(A)
p^≈N(0.64,0.0242)\hat p\approx N(0.64,0.024^2)
(B)
p^≈N(0.64,0.642)\hat p\approx N(0.64,0.64^2)
(C)
p^≈N(0.36,0.0242)\hat p\approx N(0.36,0.024^2)
(D)
p^≈N(0.64,0.0362)\hat p\approx N(0.64,0.036^2)
Question linkSyllabus coverage

Related questions

  1. Q9 · Original practice · 1 mark
    In a random sample of 200 voters, 54 support a proposal. The sample proportion is
    Sampling and proportions
  2. Q19 · Original practice · 1 mark
    For repeated samples of size 400 from a population with proportion p=0.30p=0.30, the standard deviation of p^\hat p is closest to
    Sampling and proportions
  3. Q34 · Original practice · 3 marks
    A population has proportion p=0.60p=0.60. For random samples of size 250, determine the mean and standard deviation of the sampling distribution of p^\hat p.
    Sampling and proportions
  4. Q44 · Original practice · 5 marks
    A manufacturer claims that the proportion of defective components is p=0.08p=0.08. In a random sample of 300 components, 34 are defective. Assuming the claim is correct, use a normal approximation to determine the probability of obtaining a sample proportion at least as large as the observed value. Comment on whether the result would be unusual at the 5% level.
    Sampling and proportions