When the sampling distribution of a statistic centers exactly around the parameter it estimates we can say that the statistic is which of the following? Unbiased Equal to the parameter Normally distributed Statistically significant
Question
When the sampling distribution of a statistic centers exactly around the parameter it estimates we can say that the statistic is which of the following? Unbiased Equal to the parameter Normally distributed Statistically significant
Solution
When the sampling distribution of a statistic centers exactly around the parameter it estimates, we can say that the statistic is Unbiased.
Here's why:
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A statistic is said to be an unbiased estimator of a population parameter if the mean of the sampling distribution of that statistic is equal to the parameter being estimated.
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This means that if we took many samples and calculated the statistic for each sample, and then took the average of these statistics, on average, we would be exactly correct.
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The statistic is not necessarily equal to the parameter, as individual samples may vary.
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The distribution of the statistic does not have to be normally distributed for the statistic to be unbiased.
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Statistical significance is a measure of the probability that the observed difference in a sample occurred by chance if the null hypothesis is true. It does not directly relate to whether a statistic is unbiased.
Similar Questions
First covered in Section 3.1, the concept of a 'sampling distribution' is really important in Statistics. If the centre of a sampling distribution is located at the parameter it is estimating, then we call that sampling distribution __________.Question 9Select one:a.random & unbiasedb.biasedc.minimum variance
Which of the following best describes the sampling distribution of a statistic? A normal curve, for which probabilities are obtained by standardizing. The mechanism that determines whether the random sampling was effective. A distribution of all parameters from the population that is to be randomly sampled. A distribution of all possible summary statistics from a single random sample, from the same population. A distribution of a single statistic from repeated random samples of the same size, from the same population.
We say that a point estimator is unbiased if which of the following is true? Its sampling distribution is normal. The standard deviation of its sampling distribution decreases as the sample size increases. Its value is always equal to the parameter it estimates. Its sampling distribution is centered exactly at the parameter it estimates.
A distribution of a single statistic from repeated random samples of the same size from the same population refers to which of the following? Distribution of summary statistics The normal curve Distribution of population parameters Sampling distribution of a statistic Random sampling
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.
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