Examples of using Sample proportion in English and their translations into Bulgarian
{-}
-
Colloquial
-
Official
-
Medicine
-
Ecclesiastic
-
Ecclesiastic
-
Computer
P2 with our sample proportions.
So we can actually substitute this with a sample proportion.
So our sample proportion is 0.568. or 56.8%, either one.
So let's look at the distribution of sample proportions.
So our sample proportion is 0.38, so let me write that over here.
If you do the same thing for the women, the sample proportion is going to be 0.591.
So you have your sample proportion, we're surveying a total of 2,000 people.
So the mean of the sampling distribution of the sample proportion.
So we could figure out a sample proportion over here for the men.
The sample proportion for the men minus the sample proportion of the women.
The sample of P1 minus the sample mean, or the sample proportion, of P2.
When we got this sample proportion, it was like taking a sample from this over here.
We sampled 1,000 men, sampled 1,000 women,and we got a sample proportion for each of them.
You could even view this as the sample proportion of teachers who thought that the computers were a good teaching tool.
And just to visualize it properly,let me draw the sampling distribution for the sample proportions.
So just here based on our sample proportions, or our sample means, it looks like there is a difference.
And just to be clear,when we got this sample mean here, this sample proportion, we just sampled it.
We got our sample proportion for the men minus our sample proportion for the women being 0.642 minus 0.591, that's 0.051.
So we're going to figure out the probability of actually getting our actual difference between our male sample proportion and our female sample proportion. .
So just remind ourselves, this sample proportion we got we can view as just a sample from this distribution of all of the possible sample proportions. .
But we're going to think about the sampling distribution for the difference of this sample proportion and this sample proportion.
So what we have is the square root, andthen in parentheses, our sample proportion for the men is 0.642, and then we're going to multiply that times 1 minus 0.642, close parentheses.
But if your n is suitably large, and in particular-- and this is kind of the test for it-- the test if n times p-- and in this case we're saying p is 30%-- if n times p is greater than 5, and n times 1 minus p is greater than 5,you can assume that the distribution of the sample proportion or the sample proportion distribution is going to be normal.
So we figured out the standard deviation here of our-- or the distribution of our sample proportions is going to be-- let me write this down, I will scroll over to the right a little bit-- it is 0.037.
So if we take our sample proportion, subtract from that the mean of the distribution of sample proportions and divide it by the standard deviation of the distribution of the sample proportions, we get 0.38, 0.38 minus 0.3.
So what we can do is, we can figure out that we got when we took the proportion of men and we subtracted from that the proportion of women-- So this is our sample proportion of men who, at least in our poll, said they would vote for the candidate.
So the mean of the sampling distribution for this sample proportion, for the women, which is going to be the same thing as the mean of the population, which we already saw is going to be equal to P2.
We know that the standard deviation of our sampling distribution of this statistic of the sample mean of P1 minus the sample proportion, or sample mean of P2, is equal to the square root of P1 times 1 minus P1 over 1,000, plus P2 times 1 minus P2 over 1,000.
So the standard deviation of our sample proportions, the standard deviation is going to be the square root-- let me put it this way-- it's going to be our population standard deviation, the standard deviation we're assuming with our null hypothesis divided by the square root of the number of samples we have.
Now to figure out the probability of having a sample proportion of 0.38, we just have to figure out how many standard deviations that is away from our mean, or essentially calculate a Z-statistic for our sample, because a Z-statistic or a Z-score is really just how many standard deviations you are away from the mean.
