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8. Sampling Distributions and the Central Limit Theorem Online Quiz Questions

Use this free practice quiz with 20 questions to review 8. Sampling Distributions and the Central Limit Theorem, test your knowledge, and prepare for your next test or exam.

20 questions
01
Choose one
1 point

Which description best defines a sampling distribution?

  1. A

    The observed individual values in one sample

  2. B

    The probability distribution of a statistic calculated from many possible random samples of the same size from the same population

  3. C

    All values in the population without reference to sampling

  4. D

    The measurement error of an instrument

02
Choose one
1 point

Individual delivery times have population standard deviation 12 minutes. What is the standard error of the sample mean for random samples of 36 deliveries?

  1. A

    0.5 minutes

  2. B

    1 minute

  3. C

    2 minutes

  4. D

    72 minutes

03
Choose one
1 point

If the sample size for a sample mean is multiplied by 4, what happens to its standard error, all else being equal?

  1. A

    It doubles

  2. B

    It is divided by 2

  3. C

    It is divided by 4

  4. D

    It remains unchanged

04
Choose all
1 point

Select all statements that correctly distinguish random sampling from random assignment.

  1. A

    Random sampling concerns selection from a population.

  2. B

    Random assignment guarantees that a sample represents the population.

  3. C

    Random assignment concerns allocating participants to treatments.

  4. D

    Random sampling by itself proves that a treatment caused an outcome.

05
Choose all
1 point

Select all statements that are consistent with the Central Limit Theorem as described in the material.

  1. A

    The sampling distribution of sample means can become approximately normal as sample size increases.

  2. B

    The theorem makes individual observations normally distributed.

  3. C

    The original population need not be normal for the approximation to apply.

  4. D

    The theorem removes systematic bias caused by a nonrepresentative sampling process.

06
True or false
1 point

True or false: A very large sample selected through a biased process becomes representative of the target population merely because its sample size is large.

  1. A

    True

  2. B

    False

07
True or false
1 point

True or false: If the population is normal and observations are independent, the sampling distribution of the sample mean is normal for every sample size.

  1. A

    True

  2. B

    False

08
Written response
1 point

A population has standard deviation 10 minutes. For random samples of 25 observations, enter the standard error of the sample mean in minutes.

09
Written response
1 point

When the sample size is doubled, by what exact multiplier does the standard error of a sample mean change? Enter the multiplier as an exact expression; do not give a decimal approximation.

10
Fill in the blank
1 point

For a sample mean, the sampling distribution's spread is measured by the , and its center is the .

11
Fill in the blank
1 point

A commonly used condition for approximating the sampling distribution of a sample proportion by a normal distribution is np≥np\ge and n(1−p)≥n(1-p)\ge .

12
Open ended
1 point

Explain the correct interpretation of a 95% confidence interval in repeated sampling. Also state why it is incorrect to say that one completed interval has a 95% probability of containing the fixed population parameter.

13
Choose one
1 point

When is a finite-population correction appropriate for the standard error of a sample mean?

  1. A

    A correction that increases the standard error because the population is finite

  2. B

    A correction used only when observations are independent with replacement

  3. C

    A correction that can reduce the standard error when sampling without replacement from a finite population

  4. D

    A correction that makes a biased sample representative

14
Choose one
1 point

Which statement best describes a sampling distribution?

  1. A

    The distribution of individual observations in one population

  2. B

    The distribution of a statistic across many possible samples of the same size

  3. C

    The distribution of all population parameters that could be estimated

  4. D

    The distribution of measurement errors within one sample

15
Choose one
1 point

Which statement correctly applies the Central Limit Theorem to a population that is strongly skewed?

  1. A

    The population must be normally distributed for every sample size

  2. B

    A sample of at least 30 always guarantees a normal sampling distribution

  3. C

    A large sample makes biased sampling representative

  4. D

    A sufficiently large sample can make the sampling distribution of the mean approximately normal even when the population is not normal

16
Choose one
1 point

A study randomly selects people from a target population but does not randomly assign them to treatments. What conclusion is most directly supported by the random selection?

  1. A

    Random sampling primarily supports generalizing results from a sample to a population

  2. B

    Random sampling primarily supports causal conclusions about treatment effects

  3. C

    Random assignment primarily determines whether a sample represents a population

  4. D

    Random assignment eliminates nonresponse and measurement error

17
Choose one
1 point

A sample is drawn without replacement and is a substantial fraction of a finite population. What is the effect of applying the finite-population correction to the standard error of the sample mean?

  1. A

    It increases the standard error because observations are dependent

  2. B

    It reduces the standard error because sampling a substantial fraction leaves less uncertainty

  3. C

    It leaves the standard error unchanged in every finite population

  4. D

    It changes the center of the sampling distribution but not its spread

18
True or false
1 point

True or false: If the sample size is doubled, the standard error of a sample mean is multiplied by 1/21/\sqrt{2}, approximately 0.707, assuming the population standard deviation is unchanged.

  1. A

    True

  2. B

    False

19
Written response
1 point

A population proportion is p=0.25p=0.25, and a random sample has size n=100n=100. Calculate the standard error of the sample proportion using SE(p^)=p(1−p)/nSE(\hat{p})=\sqrt{p(1-p)/n}. Enter the value rounded to four decimal places; an absolute tolerance of 0.0001 is allowed.

20
Written response
1 point

What statistical term names the standard deviation of a sampling distribution?