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# S2 Problem watch

1. Hey I would be really grateful if someone could help me out on this question.

'Boxes of the breakfast cereal Crispo indicate that they contain 375 grams. After receiving several complaints that the boxes contain less than the stated amount, a supermarket manager weighs the contents of a random sample of 40 boxes from a large consignment. The masses, x grams, of the contents are summarised by
<sum>(x - 375) = -46 and <sum>(x-375)^2 = 616. Test, at the 5% significance level, whether the mean mass of the contents of all boxes in the consignment is less than 375 grams.'

So null hypothesis: u=375
Alternative hypothesis: u<375 (where u = 'mju')

X-N(375, [s^2/40])

What I'm stuck on is how to find the sample mean using <sum>(x-375) (I can do this with the normal <sum>x) and the variance, s^2 using <sum>(x-375)^2 (again can do this with <sum>x^2). It's the dumb brackets that are causing problems.
The formula for s^2 is (n/n-1) x[(<sum>x^2/n) - (sample mean)^2).
If someone could just sort this part out of me I will be very thankful!
2. for the mean you need to do (x-375)/40 + 375

for variance just use the x-375 bit because it won't affect the variance.
3. Thank you posh git! could do the mean but didn't know what to do with variance. You've cleared it up now.. cheers![PHP]
4. Ok I take that back. I tried using 616 as Ex^2 to find s^2 but no luck! s^2 comes to a negative number so I can't square root it. Agh!
5. Let be the (unknown) variance of the mass of a randomly selected box of Crispos.

We can estimate by

(40/39) [(1/40)*616 - (-46/40)^2] = 14.439

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