Which symbol denotes the population standard deviation?

Answer: σ σ is the population standard deviation; s denotes the sample standard deviation.

The value 32/50 = 0.64 is best described as which of the following?

Answer: A statistic, p̂ Because 0.64 was computed from a sample, it is a statistic — specifically the sample proportion p̂.

Which symbol denotes the population proportion?

Answer: p p denotes the population proportion; p̂ is the sample proportion.

AP Statistics · Topic 5.4

Biased and Unbiased Point Estimates Practice

Part of Sampling Distributions.(UNC-3.E)

Practice questions

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Sample questions

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Sample 1difficulty 1/5
$Which symbol denotes the population standard deviation?$
- A
  $σ̂$
- B
  $σ_x̄$
- C
  $s$
- D
  $σ$
  check_circle
Why
$σ is the population standard deviation; s denotes the sample standard deviation.$
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Sample 2difficulty 1/5
$A random sample of 50 voters is taken from a city, and 32 of them favor a new ordinance.$
$The value 32/50 = 0.64 is best described as which of the following?$
- A
  $A statistic, x̄$
- B
  $A parameter, p$
- C
  $A parameter, μ$
- D
  $A statistic, p̂$
  check_circle
Why
$Because 0.64 was computed from a sample, it is a statistic — specifically the sample proportion p̂.$
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Sample 3difficulty 1/5
$Which symbol denotes the population proportion?$
- A
  $P_x̄$
- B
  $p̂$
- C
  $p$
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- D
  $π̂$
Why
$p denotes the population proportion; p̂ is the sample proportion.$
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Sample 4difficulty 2/5
$A statistic T is being evaluated as an estimator for a parameter θ.$
$Which statement best describes an unbiased estimator?$
- A
  $The mean of its sampling distribution equals the parameter being estimated.$
  check_circle
- B
  $Its sampling distribution is symmetric.$
- C
  $Its standard deviation is small.$
- D
  $It always equals the parameter.$
Why
$An estimator is unbiased when the mean of its sampling distribution equals the population parameter.$
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Sample 5difficulty 2/5
$A researcher computes the average height of all 1,200 students at a high school and finds it to be 65.4 inches.$
$Which symbol best represents the value 65.4 inches?$
- A
  $x̄$
- B
  $p$
- C
  $μ$
  check_circle
- D
  $p̂$
Why
$Because every student in the population was measured, 65.4 inches is a parameter — the population mean μ.$
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