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When comparing the means of matched data and large samples are taken, the differences must be Normally distributed in the population. True/False

The answer that was given in class was that it was false and i cannot understand why, I thought since the sample data was large the central limit theorem would apply and therefore the differences are normally distributed.

Sam
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  • You seem to be agreeing with the answer! Notice that "Normally distributed in the populations" and "differences are normally distributed" mean two different things. – whuber Apr 23 '21 at 16:40
  • Of likely interest: https://stats.stackexchange.com/questions/473455/debunking-wrong-clt-statement. You appear to be making the (common) mistake that some of my colleagues made last summer. – Dave Apr 23 '21 at 16:48

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