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The spread of the sampling distribution of x⎯⎯x¯ is ____________ the spread of the corresponding population...

The spread of the sampling distribution of x⎯⎯x¯ is ____________ the spread of the corresponding population distribution sampling distribution.

larger than

smaller than

the same as

exactly ½

Math   Statistics-And-Probability   
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Answer #1

=> As we increase sample size standard variation reduces and make the spread gets smaller. =>Which is clearly mentioned in central limit theorem, the sampling distribution will look more and more like normal distribution as the sample size is increased, even when the population itself is not normally distributed!

=>as we know that spread of sample mean =std deviation/sqrt(n)

=>hence The spread of the sampling distribution of x¯ is smaller than the spread of the corresponding population distribution sampling distribution.

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