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# S3 Confidence intervals watch

1. Could someone possibly help with the second and third parts?
I've got 0.3108 for the first part
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2. For the first part of the question I did:

3. (Original post by Mutleybm1996)
For the first part of the question I did:

Looks good so far.

So, we have

What then is the distribution of the sample mean for 9 observations?

The mean will be 0, but what about the variance?
4. (Original post by ghostwalker)
Looks good so far.

So, we have

What then is the distribution of the sample mean for 9 observations?

The mean will be 0, but what about the variance?
X9? I think....

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5. (Original post by Mutleybm1996)
X9? I think....

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Needs to be divided by 9, so,

You should be familiar with this - it's fairly basic for sampling.
6. (Original post by ghostwalker)
Needs to be divided by 9, so,

You should be familiar with this - it's fairly basic for sampling.
Wait, sorry, I read it as 9 different butterflies! In this case would it be x9?

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7. (Original post by Mutleybm1996)
Wait, sorry, I read it as 9 different butterflies! In this case would it be x9?

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If it was 9 different butterflies, then they'd have different weights. The error on the mean weight would have the same distribution I think, but I'm not 100% sure.
8. (Original post by ghostwalker)
Looks good so far.

So, we have

What then is the distribution of the sample mean for 9 observations?

The mean will be 0, but what about the variance?

So, we have

Then do I do the same again as for the first question?

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9. (Original post by Mutleybm1996)
So, we have

Then do I do the same again as for the first question?
Yes.

Standard, constructing a confidence interval.
10. (Original post by ghostwalker)
Yes.

Standard, constructing a confidence interval.
Doing the same again gives z=45? I think. For part b

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11. Sorted it! Thanks

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