Sampling from Non-Normal Populations
When a population is not normally distributed, the sampling distribution of the sample mean may not be normally distributed. This means that the sample mean is not always likely to be close to the population mean, and the probability of getting a sample mean that is far away from the population mean is not always very low.
The shape of the sampling distribution of the sample mean depends on the shape of the population distribution. For example, if the population distribution is skewed, the sampling distribution of the sample means will also be skewed.
The standard error of the mean is still a useful measure of how much variation there is in the sample means from sample to sample, even when the population is not normally distributed. However, the standard error of the mean may not be as accurate for non-normal populations as it is for normally distributed populations.
MCQs on Sampling from Non-Normal Populations
- What is the sampling distribution of the sample mean for a non-normal population?
- It is always normally distributed
- It is always skewed
- It is always uniform
- It can be any shape
The correct answer is: It can be any shape.
- What is the effect of increasing the sample size on the sampling distribution of the sample mean for a non-normal population?
- The sampling distribution becomes more normally distributed
- The sampling distribution becomes more skewed
- The sampling distribution does not change
- The sampling distribution cannot be determined
The correct answer is: The sampling distribution does not change.
- What is the standard error of the mean for a non-normal population?
- It is a measure of how much variation there is in the sample means from sample to sample
- It is the same as the population standard deviation
- It is always equal to zero
- It is always equal to the population mean
The correct answer is: It is a measure of how much variation there is in the sample means from sample to sample.
Tips for Sampling from Non-Normal Populations
- Remember that the sampling distribution of the sample mean may not be normally distributed for non-normal populations.
- Understand how the standard error of the mean is affected by the sample size.
- Use the standard error of the mean to make inferences about the population mean, but be aware that the results may not be as accurate as they would be for normally distributed populations.