Buzzz1325
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#1
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#1
A machine fills 1kg bags of sugar. The actual weight of each bag can be assumed to be normally distributed.

The manufacturer requires that
i) the mean weight of the contents of the bag is 1010g
ii) 95% of the bags filled contain between 1000g and 1020g of sugar

a) Show that this is equivalent to demanding that the variance of the sampling distribution, to 2dp, is equal to 26.03g^2.


A sample of 8 bags was selected at random. The weights in grams of these bags were: 1012.6, 1017.7, 1015.2, 1020.9, 1005.7, 1009.9, 1011.4.
Assuming the variance of the actual weights is 26.03g^2

b) Test at the 2% significance level to decide whether this sample provides sufficient evidence to conclude that the machine is not fulfilling condition (i).

Any advice on the method for both a) and b) would be appreciated.
Thanks.
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mqb2766
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#2
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#2
(Original post by Buzzz1325)
A machine fills 1kg bags of sugar. The actual weight of each bag can be assumed to be normally distributed.

The manufacturer requires that
i) the mean weight of the contents of the bag is 1010g
ii) 95% of the bags filled contain between 1000g and 1020g of sugar

a) Show that this is equivalent to demanding that the variance of the sampling distribution, to 2dp, is equal to 26.03g^2.


A sample of 8 bags was selected at random. The weights in grams of these bags were: 1012.6, 1017.7, 1015.2, 1020.9, 1005.7, 1009.9, 1011.4.
Assuming the variance of the actual weights is 26.03g^2

b) Test at the 2% significance level to decide whether this sample provides sufficient evidence to conclude that the machine is not fulfilling condition (i).

Any advice on the method for both a) and b) would be appreciated.
Thanks.
A. Use the range 1000:1020 to get the standard deviation, then Square to get the variance.
B. The sample mean is normally distributed with standard deviation
Sigma/sqrt(n)
Youre testing to see if the sample mean is different from 1010
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Buzzz1325
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#3
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(Original post by mqb2766)
A. Use the range 1000:1020 to get the standard deviation, then Square to get the variance.
B. The sample mean is normally distributed with standard deviation
Sigma/sqrt(n)
Youre testing to see if the sample mean is different from 1010
a) but the standard deviation comes out at 10 and variance 100. I don't see how you get it to equal 26.03?
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mqb2766
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The standard deviation would be approximately 5. Use tables to get exact value.
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Buzzz1325
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#5
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(Original post by mqb2766)The standard deviation would be approximately 5. Use tables to get exact value.

Sorry, which table did you get this from?
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mqb2766
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#6
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(Original post by Buzzz1325)
(Original post by mqb2766)The standard deviation would be approximately 5. Use tables to get exact value.

Sorry, which table did you get this from?
Mean +/- two std Devs is 20.
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Buzzz1325
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#7
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#7
(Original post by mqb2766)
Mean +/- two std Devs is 20.
I understand that but which table do I use to find the exact value?
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mqb2766
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(Original post by Buzzz1325)
I understand that but which table do I use to find the exact value?
The cumulative distribution table tells you the area under the normal pdf.
https://en.wikipedia.org/wiki/Standard_normal_table
Remember its two tailed, so you're looking for 0.475.
Make sure you understand what you're doing, what the cumulative (normal) distribution is and how it represents 67%, 95%, etc in terms of standard deviations.
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Buzzz1325
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#9
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#9
(Original post by mqb2766)
The cumulative distribution table tells you the area under the normal pdf.
https://en.wikipedia.org/wiki/Standard_normal_table
Remember its two tailed, so you're looking for 0.475.
Make sure you understand what you're doing, what the cumulative (normal) distribution is and how it represents 67%, 95%, etc in terms of standard deviations.
Thank you for clarifying. It's my first time looking at them so doing lots of practise! Thanks again for your help.
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mqb2766
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#10
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#10
(Original post by Buzzz1325)
Thank you for clarifying. It's my first time looking at them so doing lots of practise! Thanks again for your help.
No problem. You should have this table somewhere: textbook, formula sheet, ...
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