Question about statistical validity

[KevanGuy]

We did a phone survey at work for a client. He's asked me to do up a report on the results. He wants a blurb like "A sufficient return on the sample was received to provide for a statistical level of validity 19 times out of 20 +/- 1.98%."

It has been a loooong time since I took this stuff in University. I'm wondering if someone can help me figure out the +/- thing for the survey we did.

We completed 396 surveys out of about 1600 households.

Thanks in advance.

[HelloHockeyFans]

I believe there's a natural logarithm in there some where... not sure where though. Might even be a hyperbolic sine too.

[CrispyGriz]

i actually was doing this exact stuff in class today, give me a few minutes and i will figure something out for ya

[CrispyGriz]

So, if I'm on the right track, what you are looking for is a confidence interval based off the data you have provided.

a) first we need to find p(hat)=396/1600=0.2475=24.75% of the households

b) to find a 95%confidence interval we know

1-alpha=0.95
alpha=.05
alpha/2=.025
z*=1.96(using a z table)
Standard Error(SE)=1.98% or 0.0198

p=p(hat) +/- z* (SE)
p=0.2475 +/- 1.96 (0.0198)
p=0.2475 +/- 0.0388
p=0.2087,0.2863

so what that means is that you are correct 95%(19 times out of 20) that your data falls within the range of 20.87%(334) and 28.63%(459) if you have a standard error of 1.98%

I'm pretty sure this is what you need. If someone could verify that I'm right it might be a good thing because i just learned this stuff today so i may have a dumb mistake somewhere in it.

[Flashpoint]

This thread has made me feel like the dumbest man alive.

Oh, to be young and in Math 31 again...

[arsenal]

Originally Posted by CrispyGriz

So, if I'm on the right track, what you are looking for is a confidence interval based off the data you have provided.

a) first we need to find p(hat)=396/1600=0.2475=24.75% of the households

b) to find a 95%confidence interval we know

1-alpha=0.95
alpha=.05
alpha/2=.025
z*=1.96(using a z table)
Standard Error(SE)=1.98% or 0.0198

p=p(hat) +/- z* (SE)
p=0.2475 +/- 1.96 (0.0198)
p=0.2475 +/- 0.0388
p=0.2087,0.2863

so what that means is that you are correct 95%(19 times out of 20) that your data falls within the range of 20.87%(334) and 28.63%(459) if you have a standard error of 1.98%

I'm pretty sure this is what you need. If someone could verify that I'm right it might be a good thing because i just learned this stuff today so i may have a dumb mistake somewhere in it.

That sounds about right.. mind you it's been years since I looked at this stuff, and I hated stats. But confidence level is the right direction.

[KevanGuy]

Cheers Griz, I have another one for you if you dont mind.

262 out of 746.

[Fozzie_DeBear]

Originally Posted by CrispyGriz

So, if I'm on the right track, what you are looking for is a confidence interval based off the data you have provided.

a) first we need to find p(hat)=396/1600=0.2475=24.75% of the households

b) to find a 95%confidence interval we know

1-alpha=0.95
alpha=.05
alpha/2=.025
z*=1.96(using a z table)
Standard Error(SE)=1.98% or 0.0198

p=p(hat) +/- z* (SE)
p=0.2475 +/- 1.96 (0.0198)
p=0.2475 +/- 0.0388
p=0.2087,0.2863

so what that means is that you are correct 95%(19 times out of 20) that your data falls within the range of 20.87%(334) and 28.63%(459) if you have a standard error of 1.98%

I'm pretty sure this is what you need. If someone could verify that I'm right it might be a good thing because i just learned this stuff today so i may have a dumb mistake somewhere in it.

I am relearning this stuff now for the CFA level 1...I think that there is a problem though...the 396/1600 is the sample/population which you don't really need (aside from reassuring yourself that you have a sufficiently large sample to represent the population).

To get a real confidence interval we need to know the sample mean and the sample standard deviation...I think...

(I also think if I don't study more I am doomed...)

[CrispyGriz]

Originally Posted by Fozzie_DeBear

I am relearning this stuff now for the CFA level 1...I think that there is a problem though...the 396/1600 is the sample/population which you don't really need (aside from reassuring yourself that you have a sufficiently large sample to represent the population).

To get a real confidence interval we need to know the sample mean and the sample standard deviation...I think...

(I also think if I don't study more I am doomed...)

the sample standard deviation is represented within the 1.98% range provided and i think your right on the sample mean but you can use population proportion(p(hat)) instead if sample mean isn't known. At least one of my examples in class did.

So assuming my first example is right, heres the results for round 2

a) first we need to find p(hat)=262/746=0.3512=35.12% of the households

b) to find a 95%confidence interval we know

1-alpha=0.95
alpha=.05
alpha/2=.025
z*=1.96(using a z table)
Standard Error(SE)=1.98% or 0.0198

p=p(hat) +/- z* (SE)
p=0.3512 +/- 1.96 (0.0198)
p=0.3512 +/- 0.0388
p=0.3124, 0.3900

so what that means is that you are correct 95%(19 times out of 20) that your data falls within the range of 31.24%(227) and 39.00%(291) if you have a standard error of 1.98%

[kermitology]

Gaussian Distribution?

I hate stats

[Slava]

Originally Posted by Fozzie_DeBear

I am relearning this stuff now for the CFA level 1...I think that there is a problem though...the 396/1600 is the sample/population which you don't really need (aside from reassuring yourself that you have a sufficiently large sample to represent the population).

To get a real confidence interval we need to know the sample mean and the sample standard deviation...I think...

(I also think if I don't study more I am doomed...)

CFA Level 1...what do you do for a living if you don't mind my asking? (you could PM me if you prefer...just curious!)

[Fozzie_DeBear]

I work at a government agency that funds high tech research..but I eventually want to get into venture capital