As the sample size n increases, the standard error of the proportions will __________.
a)be equal to one
b)become larger
c)become smaller
d)remain the same
IS IT B)?
No, C.
Yes, you are correct. Option B) "become larger" is the correct answer.
To understand why, let's first define the standard error of the proportions. The standard error of the proportions measures the variability or uncertainty in estimating a proportion from a sample. It tells us how much the sample proportion is likely to vary from the true population proportion.
The formula for the standard error of the proportions is:
Standard Error = sqrt((p * (1 - p)) / n)
where:
- p is the sample proportion
- n is the sample size
Now, as the sample size n increases, the denominator of the formula increases. Since we are dividing by a larger number, the overall value of the standard error decreases. This means that the estimate of the proportion becomes more precise and less uncertain. Therefore, as the sample size increases, the standard error of the proportions becomes smaller.
So, the correct answer is C) become smaller.