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    Can someone please explain why for part b we time by 5 instead of 5/root n?

    I don't really understand what part b is asking, and why it's approached differently to part c where we find the confidence limits.

    Can someone please explain what's going on here
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    (Original post by Katiee224)
    Can someone please explain why for part b we time by 5 instead of 5/root n?

    I don't really understand what part b is asking, and why it's approached differently to part c where we find the confidence limits.

    Can someone please explain what's going on here
    There's a difference between confidence intervals and the standard error of the mean. You might want to look the latter term up in your S3 textbook!
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    (Original post by Katiee224)
    Can someone please explain why for part b we time by 5 instead of 5/root n?

    I don't really understand what part b is asking, and why it's approached differently to part c where we find the confidence limits.

    Can someone please explain what's going on here
    you use 5 because in the line above b) you are told that 5 is the population standard deviation

    in the question they ask for limits for which 90% of the tubes' weights lie, they dont ask for limits for which 90% of the tubes' sample/mean weight lie

    "the tubes weight" implies the whole population
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    (Original post by Zacken)
    There's a difference between confidence intervals and the standard error of the mean. You might want to look the latter term up in your S3 textbook!
    (Original post by DylanJ42)
    you use 5 because in the line above b) you are told that 5 is the population standard deviation

    in the question they ask for limits for which 90% of the tubes' weights lie, they dont ask for limits for which 90% of the tubes' sample/mean weight lie

    "the tubes weight" implies the whole population
    So because in part b I am working with the whole population and not a sample, I use the standard deviation, instead of the standard error of the mean?
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    (Original post by Katiee224)
    So because in part b I am working with the whole population and not a sample, I use the standard deviation, instead of the standard error of the mean?
    No, you want to use the standard error of the mean which is given by \frac{\sigma}{\sqrt{n}} where n is your sample size!
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    (Original post by Katiee224)
    So because in part b I am working with the whole population and not a sample, I use the standard deviation, instead of the standard error of the mean?
    thats pretty much how i think of it yea when doing s3 papers I tend to underline words/phrases such as "sample mean", "mean weight" etc because they imply using the sample distribution (and more specifically sd/root n) and you can lose big marks if you miss something like that
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    (Original post by Zacken)
    No, you want to use the standard error of the mean which is given by \frac{\sigma}{\sqrt{n}} where n is your sample size!
    isnt that whats happening here?
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    a maths disagreement with zacken, my worst fear :afraid:
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    (Original post by Zacken)
    No, you want to use the standard error of the mean which is given by \frac{\sigma}{\sqrt{n}} where n is your sample size!
    (Original post by DylanJ42)
    thats pretty much how i think of it yea when doing s3 papers I tend to underline words/phrases such as "sample mean", "mean weight" etc because they imply using the sample distribution (and more specifically sd/root n) and you can lose big marks if you miss something like that
    thank you both for the help

    so is that why when using the central limit theorem we use the standard error of the mean, because we are always dealing with a sample?
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    (Original post by DylanJ42)
    isnt that whats happening here?
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    a maths disagreement with zacken, my worst fear :afraid:
    Isn't that what I'm saying? You should use that, no? I don't actually remember any of the terminology from S3. I'll shut up and leave the OP in your hands...
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    Hehe I will go with dylans definition

    thanks for the help though guys, that has cleared up the misunderstanding
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    (Original post by Zacken)
    Isn't that what I'm saying? You should use that, no? I don't actually remember any of the terminology from S3. I'll shut up and leave the OP in your hands...
    well the only difference (really) between part b and part c is that in b) we use the population standard deviation and in part c we are using the sample standard deviation because in b) they ask for the weight (implies population) and in c) they ask for the mean weight (implies sample)

    i dont really know in the ins and outs either, thats just what ive picked up from doing past papers :laugh:

    come rescue us further pure :laugh:
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    (Original post by Katiee224)
    Hehe I will go with dylans definition

    thanks for the help though guys, that has cleared up the misunderstanding
    has it? im lost myself now
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    (Original post by Katiee224)
    Hehe I will go with dylans definition

    thanks for the help though guys, that has cleared up the misunderstanding
    right a good explanation bc I feel like ive confused you further;


     \displaystyle \text{Let}\:\: W = \text{weight of the tubes} (this is for the whole population)

    b) We are talking about the whole population for this part because it says "weights of tubes", so we must use the population distribution for this part which is;

     \displaystyle W \sim N(502.2\:, 5^2)

    You are looking for limits for which 90% of the weights lie, so we want to go to tables and find values of z which are exceeded with probability 0.05 (that is 5% each side)

    tables tell us  \displaystyle z = 1.6449

    this means that 1.6449 standard deviations either side of the mean should roughly contain 90% of the weights (do you remember learning something like this http://i.investopedia.com/inv/articl...ceinterval.gif)

    so the 90% interval which will contain roughly 90% of the weights is;  \displaystyle \text{mean}\: \pm 1.6449 \times \text{standard deviation}

    plugging in values we get  \displaystyle 502.2 \pm 1.6449 \times 5

    so interval is;  \displaystyle [493.98\:,510.42]
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    c) mean weight of tubes this time, this implies using the sample distribution; (and the sample size was 10)

     \displaystyle \bar{W} \sim N\left(502.2\:, \left(\frac{5}{\sqrt{10}}\right)  ^2\right)

    we want a 95% confidence interval this time, so we find a value of z which gives us 2.5% either side, this is  \displaystyle z = 1.96

    once again using  \displaystyle \text{mean}\: \pm 1.96 \times \text{standard deviation} and plugging in our values from the distribution we get;

     \displaystyle 502.2 \pm 1.96 \times \frac{5}{\sqrt{10}}

    so the confidence interval is;  \displaystyle [499.1\:,505.3]


    hope this helps as explaining this has helped me massively
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    (Original post by DylanJ42)
    ;


     \displaystyle \text{Let}\:\: W = \text{weight of the tubes} (
    I read "weight of lubes" for a second... time to get off the internet
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    (Original post by Zacken)
    I read "weight of lubes" for a second... time to get off the internet
    a 500g bottle of lube :eek: is that why you're awake all night yea?
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    (Original post by Zacken)
    I read "weight of lubes" for a second... time to get off the internet
    Seems our conversation is rubbing off on other threads
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    I couldn't resist
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    (Original post by Student403)
    Seems our conversation is rubbing off on other threads
    Spoiler:
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    I couldn't resist
    :toofunny: bloody hell :rofl:
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    (Original post by DylanJ42)
    hope this helps as explaining this has helped me massively
    it helped me quite a bit! nicely 'splained

    (Original post by Student403)
    Seems our conversation is rubbing off on other threads
    Spoiler:
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    I couldn't resist
    you don't have to be so anal about it
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    (Original post by DylanJ42)
    right a good explanation bc I feel like ive confused you further;


    your first explanation was actually more than perfect but now there is no doubt in my understanding at all hehe

    the s3 book just baffles me with their awful explanations so i'm trying to fill the gaps in my knowledge with past papers haha

    time for some fp2 now *gulp*
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    (Original post by Katiee224)
    your first explanation was actually more than perfect but now there is no doubt in my understanding at all hehe

    the s3 book just baffles me with their awful explanations so i'm trying to fill the gaps in my knowledge with past papers haha

    time for some fp2 now *gulp*
    well 2 explanations is better than one

    yea past papers really help a lot for S3, ive only got 4 left though :cry:

    are you doing FP3 also? :smartass:
 
 
 
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