Math Problem Statement
A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is σ = 5.
What is the standard error of the mean, σxbar?
Solution
The standard error of the mean (denoted as ) is calculated using the formula:
Where:
- is the population standard deviation (),
- is the sample size ().
Calculation:
First, calculate :
Now divide:
Final Answer:
The standard error of the mean is approximately 0.791.
Would you like more explanation or have any further questions?
Related Questions:
- How is the standard error of the mean different from the population standard deviation?
- What happens to the standard error if the sample size increases?
- How would the result change if the population standard deviation were unknown?
- Why is it important to use the sample size in calculating the standard error of the mean?
- Can the standard error be used to construct a confidence interval?
Tip:
When calculating the standard error, always verify whether the standard deviation provided is for the population () or the sample (), as they involve different treatments in the formulas.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Standard Error
Probability
Formulas
σx̄ = σ / √n
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 10-12
Related Recommendation
Calculate Standard Error for a Sample Mean with σ = 21 and n = 49
Calculate Standard Error of the Mean with σ = 44 and Various Sample Sizes
Calculate the Standard Error of the Mean for a Sample of 50 Employees
Standard Error Calculation with Finite Population Correction
Calculating Standard Error and Comparing Population vs Sample Data