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##### As a sample size approaches infinity,

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**Question**

As a sample size approaches infinity, how does the student?s t distribution compare to the normal z distribution? When a researcher draws a sample from a normal distribution, what can one conclude about the sample distribution? Explain.;I need a comment (verify solution) in 25-75 words from the response given below from the question listed above.;As the sample size increases or approaches infinity, student's t-distribution approaches to the standard normal distribution and they start to become the same because the errors in using s to estimate? decreases with larger samples.. The t-student?s distribution is used for small sample sizes. As the sample size increases the t-distribution will become more and more like the normal distribution.;The t ? distribution has similar characteristics with the z ? distribution: they are both continuous distributions, are bell ? shaped and are symmetrical. But the t ? distribution is more spread out and flatter at the center than the standard normal distribution. This is because the standard deviation of the t ? distribution is larger than the standard normal distribution. If we will draw a sample from a normal distribution, the sample distribution will also have a normal distribution with mean =? and standard deviation of?/?n.;Reference;Lind, Marchal, Wathen. Basic Statistics for Business & Economics, 7th Ed. McGraw-Hill Irwin. 2011, page 263

Paper#26454 | Written in 18-Jul-2015

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