Math Problem Statement
A random sample with size n = 9 is drawn from a population that follows normal distribution with mean of 10 and standard deviation of 6. What is the mean of all sample means of size 9?
Solution
In statistics, the mean of all sample means (also known as the expected value of the sample means) is equal to the population mean.
Given that the population has a mean (μ) of 10, the mean of all sample means for a sample size of is also:
If you have any questions or need further clarification, feel free to ask! Here are some related questions you might consider:
- How does the Central Limit Theorem apply to this scenario?
- What is the standard error of the sample means for this sample size?
- How does the sample size affect the distribution of sample means?
- What would happen if the sample size were larger or smaller?
- How can we use this information to estimate population parameters?
Tip: Understanding the properties of the sampling distribution can help in making inferences about the population from sample data.
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Math Problem Analysis
Mathematical Concepts
Statistics
Sampling Distributions
Expected Value
Formulas
Mean of sample means (\( \bar{X} \)) = Population mean (\( \mu \))
Theorems
Central Limit Theorem
Suitable Grade Level
College Level - Introductory Statistics
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