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Most probably not. But it should be close to the population mean if various conditions are met:
For example, the population should consist of independent, [nearly] identically distributed variables, the sample is not systematically biased (it does not have to be completely random).
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Why is the sample mean an unbiased estimator of the population mean?
The sample mean is an unbiased estimator of the population mean because the average of all the possible sample means of size n is equal to the population mean.
True or false a distribution of sample means is normally distributed with a mean equal to the population mean and standard deviation equal to the standard error of the mean?
True.
What is population mean in statistics?
The population mean is the mean value of the entire population. Contrast this with sample mean, which is the mean value of a sample of the population.
What happens to the sample mean as the sample size increases?
With a good sample, the sample mean gets closer to the population mean.
What does it mean for a sample to representative of a population?
That the key characteristics of the population are reflected in the sample.
Why is the sample mean an unbiased estimator of the population mean?
The sample mean is an unbiased estimator of the population mean because the average of all the possible sample means of size n is equal to the population mean.
True or false a distribution of sample means is normally distributed with a mean equal to the population mean and standard deviation equal to the standard error of the mean?
True.
When is the sample mean over repeated samples from the same population or process not normally distributed?
Provided the samples are independent, the Central Limit Theorem will ensure that the sample means will be distributed approximately normally with mean equal to the population mean.
Why do most sample means differ somewhat from the population mean?
The sample is not a perfect representation of the population.
What does randomisation mean?
It means that the every element in a population has an equal chance of being selected to be in the sample which is studied. Equivalently, in considering a sample of a particular size, every possible sample of that size has the same chance of being selected.
What is population mean in statistics?
The population mean is the mean value of the entire population. Contrast this with sample mean, which is the mean value of a sample of the population.
What does it mean to say that the sample variance provides an unbiased estimate of the population variance?
It means you can take a measure of the variance of the sample and expect that result to be consistent for the entire population, and the sample is a valid representation for/of the population and does not influence that measure of the population.
What does simple random sample mean in statistics?
It means that every member of the population has the same probability of being included in the sample.
Difference between calculating the sample mean and the population mean?
The same basic formula is used to calculate the sample or population mean. The sample mean is x bar and the population mean is mu. Add all the values in the sample or population and divide by the number of data values.
What is the best estimator of population mean?
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.
What is the difference between calculating the sample mean and the population mean?
You calculate the actual sample mean, and from that number, you then estimate the probable mean (or the range) of the population from which that sample was drawn.
What happens to the sample mean as the sample size increases?
With a good sample, the sample mean gets closer to the population mean.
