Some basic rules
Random questions
Practice problems
100
What are we looking for in the central limit theorem?
The mean of the sample, the size of the sample, and the standard deviation of the sample
100
The Central Limit Theorem is particularly useful for making inferences about populations when the population distribution is not normal. Name one type of non-normal distribution.
uniform, exponential, skewed, bimodal, etc.
100
You collect a random sample of 25 exam scores from a population with a known standard deviation of 10. What is the standard deviation of the sampling distribution of the mean?
2 (σ/√n = 10/√25 = 10/5 = 2)?
200
How will the sampling distribution of the mean be compared to the population distribution?
This distribution would be less spread out
200
When estimating the population mean using the Central Limit Theorem, what two parameters from the population do you need to know?
population mean (μ) and the population standard deviation (σ)?
200
You collect a random sample of 36 temperatures from a population with a known standard deviation of 5 degrees Celsius. What is the standard deviation of the sampling distribution of the mean?
What is 5/√36 = 5/6 = 5/6 degrees Celsius?
300
What graph do we use for our central limit theorem?
the normal distribution
300
Name two conditions that should be met for the Central Limit Theorem to apply.
random sampling and a sufficiently large sample size?
300
You gather a sample of 16 test scores from a population with a known standard deviation of 20. If you increase the sample size to 64, what happens to the standard deviation of the sampling distribution of the mean?
What is it decreases to 20/√64 = 20/8 = 2.5?
400
How will bigger samples affect your spread on the normal distribution graph?
it will be a smaller spread in the distribution
400
The Central Limit Theorem is a fundamental concept in statistics because it enables us to make inferences about population parameters using this type of data.
What is sample data?
400
If you have a sample size of 100 and you know the population standard deviation is 15, calculate the standard deviation of the sampling distribution of the mean.
What is 15/√100 = 15/10 = 1.5?
500
What is the formula for the central limit theorem?
500
When calculating the standard deviation of the sampling distribution of the mean, what should you divide the population standard deviation by?
square root of the sample size (σ/√n)?
500
You collect a random sample of 64 scores from a population with a known standard deviation of 15. What is the standard deviation of the sampling distribution of the mean?
What is 15/√64 = 15/8 = 1.875?