Sampling Distributions Quiz
Test your understanding of sampling distributions in statistics. Please answer all questions to the best of your ability.
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1. What is a sampling distribution?
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2. Which of the following best describes the mean of the sampling distribution of the sample mean?
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It is equal to the population mean.
It is equal to the population median.
It is always greater than the population mean.
Other
3. Select all characteristics of a sampling distribution of the sample mean.
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It is normally distributed if the sample size is large enough.
Its mean equals the population mean.
Its standard deviation is called the standard error.
It is always skewed.
Other
4. Calculate the standard error of the mean for a population with standard deviation σ = 10 and sample size n = 25.
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5. The Central Limit Theorem states that:
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The sampling distribution of the sample mean approaches a normal distribution as the sample size increases.
The population becomes normal as the sample size increases.
Sample means always equal the population mean.
Other
6. Match the following terms to their correct definitions.
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Rows
Term
Definition
Sampling distribution
A distribution of sample statistics computed for all possible samples of a given size from a population.
The average value of a statistic over all possible samples.
A measure of the variability of a statistic.
Other
Expected value
A distribution of sample statistics computed for all possible samples of a given size from a population.
The average value of a statistic over all possible samples.
A measure of the variability of a statistic.
Other
Standard error
A distribution of sample statistics computed for all possible samples of a given size from a population.
The average value of a statistic over all possible samples.
A measure of the variability of a statistic.
Other
7. Rate your confidence in solving sampling distribution problems.
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Not confident
1
2
3
4
Very confident
5
1 is Not confident, 5 is Very confident
8. In your own words, explain why the standard error decreases as sample size increases.
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9. Suppose you take many samples from a population. What would you expect the mean of the sample means to be close to?
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10. A population has a mean of 50 and standard deviation of 8. What is the probability that a random sample of size 16 has a mean greater than 52? (Show your calculation or reasoning.)
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