# Normal Mean Hypothesis Testing

WatchI'm familiar with the simple straightforward mean hypothesis testing but I have no idea how to do this one, thanks in advance

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#2

(Original post by

I'm familiar with the simple straightforward mean hypothesis testing but I have no idea how to do this one, thanks in advance

**Retsek**)I'm familiar with the simple straightforward mean hypothesis testing but I have no idea how to do this one, thanks in advance

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(Original post by

What do you mean by straightforward mean hypothesis testing? Are you familiar with the distribution of the sample mean?

**Notnek**)What do you mean by straightforward mean hypothesis testing? Are you familiar with the distribution of the sample mean?

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#4

(Original post by

I might not have all the terminology down, is that like how the variance of the sample mean is the variance of the population divided by the size of the sample (n)

**Retsek**)I might not have all the terminology down, is that like how the variance of the sample mean is the variance of the population divided by the size of the sample (n)

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Yes that's right. Have you ever done a hypothesis test that involves the sample mean? Are you just stuck on Q25 or can you not do the ones above it also?

**Notnek**)Yes that's right. Have you ever done a hypothesis test that involves the sample mean? Are you just stuck on Q25 or can you not do the ones above it also?

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#6

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Just 25, it's different in the way it's worded and I felt like it didn't give you all the necessary info, although my friends said it was just like the others, I would show the others so you could figure out what I mean but it was on a test and I just snapped a picture at the end

**Retsek**)Just 25, it's different in the way it's worded and I felt like it didn't give you all the necessary info, although my friends said it was just like the others, I would show the others so you could figure out what I mean but it was on a test and I just snapped a picture at the end

I can have another look tomorrow but if you need an answer now I recommend starting a new thread so that it's unanswered and someone else can help. You may not get an answer tonight though.

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(Original post by

Hmm just had another look at the question and there's one thing I need to have a think about but it's getting late. I'm still not a stats expert yet

I can have another look tomorrow but if you need an answer now I recommend starting a new thread so that it's unanswered and someone else can help. You may not get an answer tonight though.

**Notnek**)Hmm just had another look at the question and there's one thing I need to have a think about but it's getting late. I'm still not a stats expert yet

I can have another look tomorrow but if you need an answer now I recommend starting a new thread so that it's unanswered and someone else can help. You may not get an answer tonight though.

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#8

(Original post by

No worries, I'm not in any rush to figure it out, thanks for your help though

**Retsek**)No worries, I'm not in any rush to figure it out, thanks for your help though

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#9

**Retsek**)

I'm familiar with the simple straightforward mean hypothesis testing but I have no idea how to do this one, thanks in advance

Here's what I think:

The significance level is 5% which is 2.5% on either side of the distribution hence our value is .

Then we see whether we have the interval entirely below , so we test whether

If so, we can say with 95% confidence that hence accept the claim.

We can say that since the sample variance is an unbiased estimate of the population variance so we can finish it off.

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#10

(Original post by

I haven't done any of this 'significance level' and 'hypothesis testing' at all, but I've done confidence intervals at A-Level (a while ago) which might be useful here but don't take my word for it since I could be wrong somewhere.

Here's what I think:

The significance level is 5% which is 2.5% on either side of the distribution hence our value is .

Then we see whether we have the interval entirely below , so we test whether

If so, we can say with 95% confidence that hence accept the claim.

We can say that since the sample variance is an unbiased estimate of the population variance so we can finish it off.

**RDKGames**)I haven't done any of this 'significance level' and 'hypothesis testing' at all, but I've done confidence intervals at A-Level (a while ago) which might be useful here but don't take my word for it since I could be wrong somewhere.

Here's what I think:

The significance level is 5% which is 2.5% on either side of the distribution hence our value is .

Then we see whether we have the interval entirely below , so we test whether

If so, we can say with 95% confidence that hence accept the claim.

We can say that since the sample variance is an unbiased estimate of the population variance so we can finish it off.

But what you said about the sample variance being an unbiased estimate of the population variance makes sense. So Retsek I'm thinking you can do this like a standard sample mean hypothesis test with

So the sample mean will be normally distributed with

and , .

But I'm not sure though because I haven't come across this type of problem at A Level.

Tagging ghostwalker who may be able to confirm.

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#11

(Original post by

I'm not sure I fully understand what you've done since I don't know much about confidence intervals. Also I'm not sure this is a hypothesis test?

**Notnek**)I'm not sure I fully understand what you've done since I don't know much about confidence intervals. Also I'm not sure this is a hypothesis test?

But as I said, I could be wrong and this wouldn't be what's expected in the new spec most likely, so this is just me throwing ideas around to hopefully help the more appropriate approaches come about

The answer I found:

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#12

I agree with Notnek with his choice of hypotheses and the distribution of the sample mean. I believe you then, assuming the null hypothesis is true, find the probability that the sample mean is less than or equal to 19.78. If this probability is less than 0.05, then you reject the null hypothesis as it is a highly unlikely result if the sample mean is in fact 20.

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#13

(Original post by

We can say that since the sample variance is an unbiased estimate of the population variance so we can finish it off.

**RDKGames**)We can say that since the sample variance is an unbiased estimate of the population variance so we can finish it off.

The sample variance is not an unbiased estimate of the population variance.

Rather , for your unbiased estimator.

Where is the sample variance.

Also we are dealing with a small sample from a population of unknown variance and mean, albeit normal, so we need the t-distribution.

**Edited**to bring in line with Edexcel terminology.

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#14

(Original post by

I think we have a couple of issues here:

The sample variance, , is not an unbiased estimate of the population variance.

Rather , for your unbiased estimator.

Also we are dealing with a small sample from a population of unknown variance and mean, albeit normal, so we need the t-distribution.

**ghostwalker**)I think we have a couple of issues here:

The sample variance, , is not an unbiased estimate of the population variance.

Rather , for your unbiased estimator.

Also we are dealing with a small sample from a population of unknown variance and mean, albeit normal, so we need the t-distribution.

I was trying to apply A Level maths methods because I was assuming it wasn't further maths for some reason.

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#15

**ghostwalker**)

I think we have a couple of issues here:

The sample variance, , is not an unbiased estimate of the population variance.

Rather , for your unbiased estimator.

Also we are dealing with a small sample from a population of unknown variance and mean, albeit normal, so we need the t-distribution.

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#16

(Original post by

Ah this is further maths stuff which is why I don't know it yet

I was trying to apply A Level maths methods because I was assuming it wasn't further maths for some reason.

**Notnek**)Ah this is further maths stuff which is why I don't know it yet

I was trying to apply A Level maths methods because I was assuming it wasn't further maths for some reason.

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#17

(Original post by

Hmmm might be some terminology issues here.

**old_engineer**)Hmmm might be some terminology issues here.

I've always used for the population, and for the sample.

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#18

(Original post by

Isn’t this S2 not further maths?

**GCSE2016Troop**)Isn’t this S2 not further maths?

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#19

(Original post by

Maybe it's in S2 I don't know. I only know new spec stats and this would be further maths.

**Notnek**)Maybe it's in S2 I don't know. I only know new spec stats and this would be further maths.

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#20

(Original post by

Yeah it’s S2 hypothesis testing on old spec

**GCSE2016Troop**)Yeah it’s S2 hypothesis testing on old spec

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