# more on sampling

• Dec 28th 2007, 03:26 AM
0123
more on sampling
I do not understand where I mistake.

The excercice says:

a philosophy course was taken by 250 students. Each memeber of a random sample of 50 students was asked to estimate the amount of time he spent on the previous week assignment. Suppose that the population standard deviation is 30 minutes.
A) What is the probability that the sample mean exceed the population mean by more than 2.5 minutes?
B) what is the probability that the sample mean is by more than 5 minutes below the population mean?
C) what is the probability that the sample mean differs from the population mean by more than 10 minutes?

Okay. For A I do P(s> p+ 2.5) so P(Z> (p+2.5-p)/(30/Squareroot50) ) look at the table and get 0.2776 but the book says 0.2546.
For B I get 0.121 but the book says 0.0951.

Where am I wrong? :( Thank you for your help.
• Dec 28th 2007, 08:57 AM
TKHunny
50/250 = 25% >> 5%! You should be using a Finite Population Correction Factor.

Sample Mean Standard Error is $\frac{30}{\sqrt{50}}*\sqrt{\frac{250-50}{250-1}}$

It's not exactly the book's answer, but it's much closer. There are also some rounding issues going on. If I round the normalized deviations to only two decimal places, I match the book exactly.

Never forget the Finite Population Correction Factor, otherwise your sample size calculation may require you to sample more than 100% of the population. That's no good, right?
• Dec 28th 2007, 10:26 AM
0123
Quote:

Originally Posted by TKHunny
50/250 = 25% >> 5%! You should be using a Finite Population Correction Factor.

Sample Mean Standard Error is $\frac{30}{\sqrt{50}}*\sqrt{\frac{250-50}{250-1}}$

what's this? why are you dividing by square root of 50?
How do I know when I need to use the Finite correction?

Thank you so much for your help and patience TKHunny.
• Dec 31st 2007, 10:07 AM
TKHunny
Divide by sqrt(50)? Simple. Law of Central Tendency. Larger the sample, smaller the variance.

FPCF? The emperical rule is 5%. If you're sampling more than that, use the factor.