Statistics - Confidence Interval???

ShaShaBear

I'm not really sure if this is the right place - I'm repeating Statistics next month to get into third year, and I am truly just as baffled as I was sitting the original exam. Let's just be clear, we've all been teaching ourselves as the lecturer is terrible. No way to fix that or report it etc, I just need to figure this out on my own time.

So, I've started with confidence intervals because they come up most often. Picked one question to do, finished it, and used an online calculator to compare answers - wrong.
I've worked forwards, backwards, legways - I can't figure out where, or even if, I'm going wrong. Here's what I know and got from it (and the question):

Q. A lab tests a random sample of 4 burgers, which gives a mean sodium content of 310mg and a standard deviation of 36mg. Find the 95% confidence interval for the mean sodium content of burgers.

1. I know the confidence level is 95, and the statistic is 310. I was then asked for the margin of error, which I was told I could get two ways.
2. Got the critical value as being 2.353 from a T-Table, and then worked out the margin of error to be 42.354.
3. Used an online calculator (http://www.mccallum-layton.co.uk/stats/ConfidenceIntervalCalc.aspx) which told me the answer should be 35.28

So, I don't know if the calculator is just dodgy, and I am right (in which case, no worries, I know how to do it now) or if its right (in which case, I have no idea how I am getting it wrong).

Any ideas or suggestions?
I should point out I am VERY SLOW when it comes to maths and statistics, so a simple explanation would be preferred :rolleyes:

nothing

Ok, first thing is that when you look up the t-tables, it needs to be for n-1 (so in this case 4-1 = 3), and then under 0.025 (for two tail to be 95%) which gives 3.182, this may be where you got tripped up.

You're using two tails because you're not looking just for either higher or lower, but both.

Next, you need to divide your standard deviation by the square root of the sample size to get the standard error; 36/sqrt(4) = 18. I can see that you did this.

Anyway, the answer is +- 57.276. You were pretty much there, just off a tiny bit with the t-value, so you have the method down.

The online calculator did not take into account the sample size for it's t-value, and it simply uses 1.96 each time (which only applies to large sample sizes).

ShaShaBear

Thank you so, so, so much - you have literally made my day! I have been getting these wrong literally all week, and I've clearly been making the same mistake every single time! You're a star

On a side note, know of any calculators that would give me the correct answer? So I can check over the next ones I do?

**Timbuk2**

This one looks like it should work, I haven't tried it though!
http://easycalculation.com/statistics/confidence-limits-mean.php

nothing

Sorry, most of the online ones I know use the 1.96 as standard, and I only work with big figures myself (have an excel program that works them all out for me... )

Once you've got the right method, you should be fine Maybe check if there are solutions to past papers? That might help you check.

Edit: The one posted above does indeed work.

ShaShaBear

That one is giving me a massive answer for the current question :eek:

EDIT: Which clearly means I'm using it wrong!

nothing

ShaShaBear wrote: »

That one is giving me a massive answer for the current question :eek:

EDIT: Which clearly means I'm using it wrong!

For the question you posted, it gives 310 +- 57.276 (the actual confidence interval)

If you want to work backwards to get the margin of error, just take the mean away from the larger number (or take the smaller number away from the mean). It basically skips a step that you need to show. Don't panic

Also, when you have a small n (so 4 here) the confidence interval will be quite big, as it is less precise than when you have a bigger sample. Hope that makes sense.

ShaShaBear

nothing wrote: »

For the question you posted, it gives 310 +- 57.276 (the actual confidence interval)

This is so silly, but can you tell me what figures you're putting where in this calculator? Im getting something completely different, so I'm making a boo-boo somewhere! :rolleyes:

Sorry about all of this!

nothing

ShaShaBear wrote: »

This is so silly, but can you tell me what figures you're putting where in this calculator? Im getting something completely different, so I'm making a boo-boo somewhere! :rolleyes:

Sorry about all of this!

no problem

your sample size is 4 (i.e. the number of burgers used to get the statistics)
the mean is 310
the standard deviation is 36

Also make sure that the drop down menu for the size of the interval is set at 95% (It seems to default at 90)

then the result is given as
310 - 57.276 < mu < 310 + 57.276

Any better?

ShaShaBear

Clearly me and the internet need to have a wee talk

**Timbuk2**

That's fine, it's the same as nothing posted

(310 - 57.276) < mu < (310 + 57.276)

= 252.724 < mu < 367.276

ShaShaBear

Oh.








....
OOHHHHHH!!!
I get it now!
Jebus Crust, I'm stupid

Thanks both of you, means a lot!