Slovin's Formula: Need Help

[emjee17]

Guys and gals, unsaon pag derive ani nga formula:

n=N/1+ Nesquared (Slovin's Formula)

legend:
n= sample size
N= population
e=margin of error

unsaon pag kuha sa e? ug sa N?

silbi naay problem nga ang e ra ang kuhaon, ang N ug n kay given na.
naa pud problem nga ang N ang gipangita thn given na ang e ug n..

please! I need your help, assignment nako is due this Wednesday.. tabang guys.. =(

[urejiak]

I don't know if sakto ba ni...

n = N /1+Ne^2
1+Ne^2(n=N/1+Ne^2)1+Ne^2
n+nNe^2=N
n=N-nNe^2
n/(1-ne^2)=N(1-ne^2)/(1-ne^2)
N=n/(1-ne^2)

n = N / 1+Ne^2
1+Ne^2(n=N/1+Ne^2)1+Ne^2
n+nNe^2 = N
nNe^2/nN=N-n/nN
e^2=(N-n)/nN
e= square root of ((N-n)/nN)

[deaf_guitarist]

i transporse ra ni?

n = (N/1) + (N)(e^2)

e = Euler's number = 2.718281828... (constant ni nga irrational number)

>>>> then, N = (n/(1 + e^2))

sakto ni?> hehe

[prukutung]

i think transposition rah ang gamiton ani... never encountered this formula before...
no idea sa nature ani... but if the formula is given and parameters are already given
then naturally you only have to apply and manipulate the formula, say transposition... ^^

[emjee17]

Thanks mga bro! hehe..

Anyway, kuya urejiak (kuya lang ko ha?)

"I don't know if sakto ba ni...

n = N /1+Ne^2
1+Ne^2(n=N/1+Ne^2)1+Ne^2
n+nNe^2=N
n=N-nNe^2
n/(1-ne^2)=N(1-ne^2)/(1-ne^2)
N=n/(1-ne^2)

n = N / 1+Ne^2
1+Ne^2(n=N/1+Ne^2)1+Ne^2
n+nNe^2 = N
nNe^2/nN=N-n/nN
e^2=(N-n)/nN
e= square root of ((N-n)/nN) "

Pareha tag formula sa e pero sa N lahi.

Akong gipang answeran ang mga problems nga e ang gi pangita, accurate man bisan inig check pud if tugma ba sa given nga N ug n.

Here are the problems diay..
1)Compute for the margin of error to be used if 800 sample units are required from a population of 2,400.

Given:
N=2,400
n=800
e=?

e= square root of N-n/Nn
= square root of 2400-800/(2400)(800)
e= 2.89%

Check:
n=N/1+Nesquared
= 2400/1+(2400)(.0289squared)
= 2400/3.004504
=798.800
n=800 >>correct!

2) A researcher plans to get 588 sample units from a population N using a 4% margin of error. What is the value of the population N?

MY derived formula:
N=n+Ne^2 n (ako ra gi cross multiply)

N= 588 + N (.04^2) (58
= 588 + .9408 N
N-.9408N = 588
.0592N = 588_
.0592 .0592
N= 9, 932

Check:
n=N/1+Nesquared
= 9932/ 1+ (9932)(.04^2)
= 9932/ 16.8912
= 587.998
n= 588 >> correct!

Your formula:
N=n/(1-ne^2)
= 588/ 1-(58(.04^2)
= 588/ .0592
= 9,932. (same answer)


But the problem lies here:
3) If the sample size is 500 and the target population is 8,000, what is the required margin of error?

e= square root of N-n/Nn
= square root of 8,000-500/(8000)(500)
= square root of 7500/4,000,000
e= 4%

Check:
n=N/1+Nesquared
=8,000/1+(8000)(.04^2)
=8,000/ 13.8
= 579.7101449
n=580 >> sobra ug 80 ang sample size.. okay ra ni?

[comptech21]

can u give me a other sample of this problem
this is the given of this problem
given:e=5% n=900 N=?
pls help me guys

[comptech21]

i need ur answer or ideas plllllllllsssssssssssssss help me guys...........

[gannie]

If you mean this formula


then by multiplying both sides by 1 + Ne^2, we get

n(1 + Ne^2) = N (A)

which can be simplified by distributing n and we will have

n + nNe^2 = N . . . (B)

Since we are looking for N, by means of transposition,
the equation will become

nNe^2 - N = - n . . . (C)

By factoring for N, we get

N(ne^2 - 1) = - n . . . (D)

And finally by dividing both sides by ne^2 - 1,

N = - n / (ne^2 - 1) . . .


For e . . . we can just start at (B) above

n + nNe^2 = N . . . (1)

By transposition we have

nNe^2 = N - n . . . (2)

Since we are looking for e, we need to isolate it
by dividing both sides by nN and the equation becomes

e^2 = (N - n) / nN . . . (3)

And then by extracting the square root of both
sides of the equation :

e = sqrt of [ (N - n) / nN ]

I hopethis can help . . .

[darellonline]

[QUOTE=gannie;10358055]If you mean this formula


then by multiplying both sides by 1 + Ne^2, we get

n(1 + Ne^2) = N (A)

which can be simplified by distributing n and we will have

n + nNe^2 = N . . . (B)

Since we are looking for N, by means of transposition,
the equation will become

nNe^2 - N = - n . . . (C)

By factoring for N, we get

N(ne^2 - 1) = - n . . . (D)

And finally by dividing both sides by ne^2 - 1,

N = - n / (ne^2 - 1) . . .


Question: what if ne^2 = a positive number larger than one, it would make N resulting to a negative answer?

[kollen]

[QUOTE=darellonline;12934786]

If you mean this formula


then by multiplying both sides by 1 + Ne^2, we get

n(1 + Ne^2) = N (A)

which can be simplified by distributing n and we will have

n + nNe^2 = N . . . (B)

Since we are looking for N, by means of transposition,
the equation will become

nNe^2 - N = - n . . . (C)

By factoring for N, we get

N(ne^2 - 1) = - n . . . (D)

And finally by dividing both sides by ne^2 - 1,

N = - n / (ne^2 - 1) . . .


Question: what if ne^2 = a positive number larger than one, it would make N resulting to a negative answer?

I agree... using the given numbers of e=5% and a sample size (n) of 900 will yield a negative value for the population (N). -720 to be exact. Anyone?