Because the whole population might be too large to sample. A good example is the population of the world. At nearly 7 billion people, it would be unrealistic to sample each person to determine some factor that you are looking at. Generally, we sample a subset of the population, taking into account differences (or errors) that might result, in this case, regional and cultural, in order to estimate the behavior of the larger population.
Yes. You could have a biased sample. Its distribution would not necessarily match the distribution of the parent population.
A simple random sample.
No, that would be a random sample.
INFERENCES Any calculated number from a sample from the population is called a 'statistic', such as the mean or the variance.
The sampling error is the error one gets from observing a sample instead of the whole population. The bigger it is, the less faith you should have that your sample represents the true value in the population. If it is zero, your sample is VERY representative of the population and you can trust that your result is true of the population.
Because the whole population might be too large to sample. A good example is the population of the world. At nearly 7 billion people, it would be unrealistic to sample each person to determine some factor that you are looking at. Generally, we sample a subset of the population, taking into account differences (or errors) that might result, in this case, regional and cultural, in order to estimate the behavior of the larger population.
First you have chose an estimator for what you want to know about the population. In general the level of variability in the result that any estimator provides will depend on the variability in the population. Therefore, the greater the variability in the population the larger your sample size must be. You will also need to decide how much precision is required in your estimate. The more precision you require the greater your sample size will have to be.
Sampling bias occurs when the sampling frame does not reflect the characteristics of the population which is being tested. Biased samples can result from problems with either the sampling technique or the data-collection method. Essentially, the group does not reflect the population which is supposed to be represented in the given survey or test. For example: If the question being asked in a survey was "do American's prefer Coca-Cola or Pepsi?" and all people asked were under 18 and from California, there would be a sampling bias as the sampling frame would not accurately represent "American's".
If the sample is not representative of the population, then the characteristics of the sample are not the characteristics of the population. Example: If I want to estimate the percentage of the population that are men, and my sample is the school's football team, my estimate would be that 100% of the population is comprised of men. What went wrong with my survey ? Simple. The football team is not a representative sample of the population, at least not as regards gender.
Yes. You could have a biased sample. Its distribution would not necessarily match the distribution of the parent population.
To avoid sampling error, you should ensure that your sample is representative of the population, use random sampling techniques, increase the sample size when possible, and use stratified sampling if your population can be divided into subgroups. Additionally, verify the reliability of your data collection methods to minimize errors.
The best estimator of the population mean is the sample mean. It is unbiased and efficient, making it a reliable estimator when looking to estimate the population mean from a sample.
A simple random sample.
Sample size is the number of samples arawn from a population. If you drew 20 samples, your sample size would be 20.
Sample is preferred to population because observing the population can be impossible due to its size. You take a random sample of the population and, with statistics, you can infer things about that population to various degrees of confidence based on the sample size and on other knowledge about the population. For instance, if you wanted to know how many people on earth have brown hair, you would not check all 6 billion people - you would create a sample set, say a few hundred, thousand, or whatever - count the number with brown hair - and then run your calculations.
The sample consisted of the entire population.