statistics 3 (edexcel) help

Original post by Katiee224

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! :smile:

Reply 2

Original post by Katiee224

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

Reply 3

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! :smile:

Original post by DylanJ42

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? :smile:

Reply 4

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? :smile:

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! :smile:

Reply 5

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? :smile:

thats pretty much how i think of it yea :biggrin:

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

Reply 6

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! :smile:

isnt that whats happening here?

Spoiler

Reply 7

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! :smile:

Original post by DylanJ42

thats pretty much how i think of it yea :biggrin:

thank you both for the help :smile:

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?

Reply 8

Original post by DylanJ42

isnt that whats happening here?

Spoiler

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... :tongue:

Reply 9

Hehe I will go with dylans definition :wink:

thanks for the help though guys, that has cleared up the misunderstanding :h:

Reply 10

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... :tongue:

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:

Reply 11

Original post by Katiee224

Hehe I will go with dylans definition :wink:

thanks for the help though guys, that has cleared up the misunderstanding :h:

has it? im lost myself now :tongue:

Reply 12

Original post by Katiee224

Hehe I will go with dylans definition :wink:

thanks for the help though guys, that has cleared up the misunderstanding :h:

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/articles/site/C2CFAconfidenceinterval.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]

.
.
.
.
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 :biggrin:

as explaining this has helped me massively

Reply 13

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

Reply 14

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? :h:

Reply 15

Student403

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

Spoiler

Reply 16

Original post by Student403

Seems our conversation is rubbing off on other threads

Spoiler

bloody hell :rofl:

Reply 17

Ayman!

Original post by DylanJ42

hope this helps :biggrin:

as explaining this has helped me massively

it helped me quite a bit! nicely 'splained :biggrin:

Original post by Student403

Seems our conversation is rubbing off on other threads

Spoiler

you don't have to be so anal about it

Reply 18

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 :smile:

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*

Reply 19