Probability of a Population greater than the one of a sample

[SV7]

I'm working on my statistics homework. The professor gave us two problems with the same probability (p), but with different number of trials (n); p= .3 and n= 2 in one and n= 200 in the other one.

He told us one was the actual population and the other one was a sample.

I did both problems and I'm pretty sure I did everything correctly. The only thing I still can't fully understand is why the population probability is higher than one of a sample??

Thank you in advance

 

[Mark44]

I'm working on my statistics homework. The professor gave us two problems with the same probability (p), but with different number of trials (n); p= .3 and n= 2 in one and n= 200 in the other one.

He told us one was the actual population and the other one was a sample.

I did both problems and I'm pretty sure I did everything correctly. The only thing I still can't fully understand is why the population probability is higher than one of a sample??

Why do you say that the population probability is larger than that of a sample? Earlier you said that you had two problems with the same probability.

 

[SV7]

Why do you say that the population probability is larger than that of a sample? Earlier you said that you had two problems with the same probability.

Right, I guess I didn't make my question clear enough sorry. We had to tell the probability of 1 of the 2 people having a disease and of 100 out of the 200 people. My question was, why is the answer higher for the population than it was for the sample, if they have the same probability and we're trying half of both?

 

[Mark44]

There are a couple of things going on here: sample statistic vs. population statistic. For a given population the various statistics (e.g., mean, standard deviation, etc.) have certain values. For a sample taken from that population the same statistics typically have different values.

For example, in the population (size n = 200), 30% have a particular disease (p = .3). If you take a sample of size n = 2, there are various possibilities:
0 people have the disease.
1 person has the disease.
2 people have the disease.
The sample value of p will be 0, .5, or 1, respectively. All of these values are different from the population value of p, which is .3.