# Confidence intervals help

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#1
1

The contents of jars of honey may be assumed to be normally distributed. The contents, in grams, of a random sample of 8 jars were as follows:

458, 450, 457, 456, 460, 459, 458, 456

a) Calculate a 95% confidence interval for the mean contents of all jars:

95% CI:

x̅ = 456.75 Sx: 3.059 n = 8 ν = 7

using calculator: Multiplier = 2.365

95% CI = 456.75 +- 2.365 x (3.059)/root(8)

= (454.192, 459.308).

b) On each jar it states `contents 454 grams.' Comment on this statement using the given sample and your results to part a):

Evidence from part a) shows that the mean is above 454g, but some jars will contain less.

c) Given that the mean contents of all jars is 454 grams, state the probability that a 95% confidence interval calculated from the contents of a random sample of jars will not contain 454 grams.:

Really not sure how to do this, any hints/help?
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1 year ago
#2
(Original post by TAEuler)
1

The contents of jars of honey may be assumed to be normally distributed. The contents, in grams, of a random sample of 8 jars were as follows:

458, 450, 457, 456, 460, 459, 458, 456

a) Calculate a 95% confidence interval for the mean contents of all jars:

95% CI:

x̅ = 456.75 Sx: 3.059 n = 8 ν = 7

using calculator: Multiplier = 2.365

95% CI = 456.75 +- 2.365 x (3.059)/root(8)

= (454.192, 459.308).

b) On each jar it states `contents 454 grams.' Comment on this statement using the given sample and your results to part a):

Evidence from part a) shows that the mean is above 454g, but some jars will contain less.

c) Given that the mean contents of all jars is 454 grams, state the probability that a 95% confidence interval calculated from the contents of a random sample of jars will not contain 454 grams.:

Really not sure how to do this, any hints/help?
Not got the model solution, but I would imagine that b) would require a bit more quantitative discussion. Probably invove the fact that the stated weight is outside the 95% confidence interval but this is based on only 8 data points. It may also mention its underestimating the "true" mean weight.

95% confidence interval is that the mean value lies within this interval, so what is the probability it lies outside this interval?
Last edited by mqb2766; 1 year ago
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#3
(Original post by mqb2766)
Not got the model solution, but I would imagine that b) would require a bit more quantitative discussion. Probably invove the fact that the stated weight is outside the 95% confidence interval but this is based on only 8 data points. It may also mention its underestimating the "true" mean weight.

95% confidence interval is that the mean value lies within this interval, so what is the probability it lies outside this interval?
It's the same as the answer in the back

And obviously that's 0.05, but 454 isn't included in that interval, and part c seems to be what's the P of it not being 454, not the P of it not being in the CI from a)
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