Contents
What is population proportion and sample proportion?
If M individuals from the population belong to a certain group, we say that the proportion of the population that belongs to this group is p = M/N. That is, the mean or expected value of the sample proportion is the same as the population proportion.
How do you find a sample proportion?
- The sample proportion is the number x of orders that are shipped within 12 hours divided by the number n of orders in the sample:
- Since p = 0.90, q=1−p=0.10, and n = 121,
- Using the value of ˆP from part (a) and the computation in part (b),
Is the sample proportion The mean?
The sample proportion is a random variable: it varies from sample to sample in a way that cannot be predicted with certainty. Viewed as a random variable it will be written ˆP. It has a mean μˆP and a standard deviation σˆP. In the same way the sample proportion ˆp is the same as the sample mean ˉx.
How to calculate the proportion of a sample?
We denote the population proportion by p, and the sample proportion by p̂. To calculate the value of p̂ from a sample of size n, simply count the number of people, x, in the population that satisfy the required condition and divide by the size of the sample, n. In symbols:
How is the proportion of the population calculated?
In the real world, you usually don’t know facts about the entire population and so you use sample data to estimate p. This sample proportion is written as p̂, pronounced p-hat. It’s calculated in the same way, except you use data from a sample: just divide the total number of items in the sample by the number of items you’re interested in.
Do you need a minimum sample size to estimate population proportion?
This is the minimum sample size you need to estimate the true population proportion with the required margin of error and confidence level. Note that if some people choose not to respond they cannot be included in your sample and so if non-response is a possibility your sample size will have to be increased accordingly.
How to calculate standard error for population proportion?
The standard error calculation involves estimating the true standard deviation by substituting the sample proportion for the population proportion in the formula. Luckily, this works well in situations where the normal curve is appropriate [i.e. when np and n (1-p) are both bigger than 5].