# Probability of a Population greater than the one of a sample

• SV7
In summary: This means that the sample statistic (p) is less than the population statistic (p). This is because the population is composed of a larger number of cases, and thus has a greater chance of having a particular value for p.
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??

Last edited:
SV7 said:
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.

Mark44 said:
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?

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.

## 1. What is the probability of a population being greater than a sample?

The probability of a population being greater than a sample depends on the specific characteristics of the population and the sample. It is important to note that the sample is just a small portion of the population and may not accurately represent the entire population. Therefore, it is not possible to determine the exact probability without knowing more information about the population and sample.

## 2. How do you calculate the probability of a population being greater than a sample?

The calculation of the probability of a population being greater than a sample involves using statistical methods such as hypothesis testing and confidence intervals. These methods take into account factors such as sample size, standard deviation, and mean to determine the likelihood of the population being greater than the sample.

## 3. Can the probability of a population being greater than a sample be 100%?

In most cases, it is not possible for the probability of a population being greater than a sample to be 100%. This is because there is always a chance that the sample may not accurately represent the entire population. However, in some cases where the sample size is very large and the sample is randomly selected, the probability may be very close to 100%.

## 4. How does the size of the sample affect the probability of a population being greater than a sample?

The size of the sample can have a significant impact on the probability of a population being greater than a sample. A larger sample size generally leads to a more accurate representation of the population, which in turn can result in a higher probability of the population being greater than the sample. However, other factors such as the variability of the population and the sampling method used also play a role in determining the probability.

## 5. What are some factors that can influence the probability of a population being greater than a sample?

Some factors that can influence the probability of a population being greater than a sample include the size and representativeness of the sample, the variability of the population, and the sampling method used. Other factors such as the level of confidence and the type of statistical analysis being performed can also impact the probability. It is important to carefully consider all of these factors when interpreting the probability of a population being greater than a sample.

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