# S3 question - assumptions

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Hi guys ,

I’m stuck on the questions I have circled . I’m trying to be careful in the wording for these assumption questions as they are quite specific . What I don’t understand is when we do and don’t assume sample means are normally distributed. Like in 19b , the answer was about how we don’t assume weight loss follows a normal distribution . Why don’t we assume this ?

Similar sort of thing for the next question . The answer was that sample sizes are large so CLT guarantees sample means are approx normally distributed. Why is this guaranteed and when wouldn’t it be guaranteed? It also says no assumptions are being made

Thanks a lot

Hi guys ,

I’m stuck on the questions I have circled . I’m trying to be careful in the wording for these assumption questions as they are quite specific . What I don’t understand is when we do and don’t assume sample means are normally distributed. Like in 19b , the answer was about how we don’t assume weight loss follows a normal distribution . Why don’t we assume this ?

Similar sort of thing for the next question . The answer was that sample sizes are large so CLT guarantees sample means are approx normally distributed. Why is this guaranteed and when wouldn’t it be guaranteed? It also says no assumptions are being made

Thanks a lot

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#2

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Hi guys ,

I’m stuck on the questions I have circled . I’m trying to be careful in the wording for these assumption questions as they are quite specific . What I don’t understand is when we do and don’t assume sample means are normally distributed. Like in 19b , the answer was about how we don’t assume weight loss follows a normal distribution . Why don’t we assume this ?

Similar sort of thing for the next question . The answer was that sample sizes are large so CLT guarantees sample means are approx normally distributed. Why is this guaranteed and when wouldn’t it be guaranteed? It also says no assumptions are being made

Thanks a lot

**Angels1234**)https://postimg.cc/gallery/umtprcvg/

Hi guys ,

I’m stuck on the questions I have circled . I’m trying to be careful in the wording for these assumption questions as they are quite specific . What I don’t understand is when we do and don’t assume sample means are normally distributed. Like in 19b , the answer was about how we don’t assume weight loss follows a normal distribution . Why don’t we assume this ?

Similar sort of thing for the next question . The answer was that sample sizes are large so CLT guarantees sample means are approx normally distributed. Why is this guaranteed and when wouldn’t it be guaranteed? It also says no assumptions are being made

Thanks a lot

Gregorius

Notnek

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#3

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Hi guys ,

I’m stuck on the questions I have circled . I’m trying to be careful in the wording for these assumption questions as they are quite specific . What I don’t understand is when we do and don’t assume sample means are normally distributed.

**Angels1234**)https://postimg.cc/gallery/umtprcvg/

Hi guys ,

I’m stuck on the questions I have circled . I’m trying to be careful in the wording for these assumption questions as they are quite specific . What I don’t understand is when we do and don’t assume sample means are normally distributed.

The central limit theorem tells you that if you draw samples of size n from an underlying population, then the mean of those samples will be distributed closer and closer to a normal distribution as n get larger and larger. This applies whatever the original distribution of observations was (provided that the original distribution meets some mathematical requirements).

Like in 19b , the answer was about how we don’t assume weight loss follows a normal distribution . Why don’t we assume this ?

Similar sort of thing for the next question . The answer was that sample sizes are large so CLT guarantees sample means are approx normally distributed. Why is this guaranteed and when wouldn’t it be guaranteed? It also says no assumptions are being made

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(Original post by

This is stuff you don't need to know at your level, but there are various forms of the central limit theorem that demand that various conditions should apply to the underlying distribution for the result to follow. One example of these conditions is for the underlying distribution to have a finite mean and a finite variance.

**Gregorius**)This is stuff you don't need to know at your level, but there are various forms of the central limit theorem that demand that various conditions should apply to the underlying distribution for the result to follow. One example of these conditions is for the underlying distribution to have a finite mean and a finite variance.

.. and this is where my confusion comes in . Is N is sufficiently large how do we know when to say hat sample means are normally distributed and when to say we don’t assume sample means are normally distributed. Does it no longer become an assumption after n gets very big .

Thanks again

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The thing is usually in questions where the sample sizes of the 2 populations are large it asks the relevance of the central limit theorem . I normally go for like as n is sufficiently large CLT allows us to assume the sample means are normally distributed. So how would our answer change if N was smaller . Because we only assume sample means are approx normally distributed providing n is large .

**Angels1234**)The thing is usually in questions where the sample sizes of the 2 populations are large it asks the relevance of the central limit theorem . I normally go for like as n is sufficiently large CLT allows us to assume the sample means are normally distributed. So how would our answer change if N was smaller . Because we only assume sample means are approx normally distributed providing n is large .

The modern approach to small sample size problems is to use computer simulation to calculate a numerical approximation to the sampling distribution to the mean. That is, actually draw many small samples from a population, calculate their means and use their empirical distribution as the sampling distribution of the mean.

.. and this is where my confusion comes in . Is N is sufficiently large how do we know when to say hat sample means are normally distributed and when to say we don’t assume sample means are normally distributed. Does it no longer become an assumption after n gets very big .

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