Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population?Review LaterValues of a parameter will vary from sample to sample but values of a statistic will notValues of both a parameter and a statistic may vary from sample to sampleValues of a parameter will vary according to the sampling distribution for that parameter.Values of a statistic will vary according to the sampling distribution for that statistic.
Question
Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population?Review LaterValues of a parameter will vary from sample to sample but values of a statistic will notValues of both a parameter and a statistic may vary from sample to sampleValues of a parameter will vary according to the sampling distribution for that parameter.Values of a statistic will vary according to the sampling distribution for that statistic.
Solution
The correct statement is: "Values of a statistic will vary according to the sampling distribution for that statistic."
Here's why:
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A parameter is a fixed value that describes a characteristic of a population. It does not vary from sample to sample because it is a constant value for a given population.
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A statistic, on the other hand, is a value that describes a characteristic of a sample. Since samples can vary, the value of a statistic can also vary from sample to sample.
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The variation in the values of a statistic from sample to sample follows a specific pattern known as the sampling distribution for that statistic.
So, the statement "Values of a statistic will vary according to the sampling distribution for that statistic" is correct.
Similar Questions
Which of the following statements best describes the relationship between a parameter and a statistic?Question 17Select one:a.A parameter has a sampling distribution with the statistic as its mean.b.A parameter has a sampling distribution used to determine values a statistic may have in repeated samples.c.A statistic is used to estimate a parameter.d.A parameter is used to estimate a statistic.
A distribution of a single statistic from repeated random samples of the same size from the same population refers to which of the following?Group of answer choicesDistribution of summary statisticsRandom samplingDistribution of population parametersThe normal curveSampling distribution of a statistic
Which one of the following is incorrect? 1.Variance of population is a parameter. 2.Standard deviation of a population is a parameter. 3.Mean of a sample is a parameter. 4.Standard deviation of a sample is a statistic.
Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. The distribution will be normal as long as the population distribution is normal. The distribution's mean is the same as the population mean 60. The distribution's standard deviation is larger than the population standard deviation of 8.
Is this statement true or false?"Parameters" relate to populations, while "statistics" relate to samples.
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