Math Problem Statement
An experiment involves randomly selecting a sample of 256 middle managers for study. One item of interest is their mean annual income. The sample mean is computed to be $35,420 and the sample standard deviation is $2,050. What is the standard error of the mean?
Solution
The standard error of the mean (SEM) is calculated using the formula:
where:
- is the sample standard deviation
- is the sample size
In this problem:
Substitute these values into the formula:
Thus, the standard error of the mean is:
Would you like more details on this calculation or have any questions?
Related Questions:
- How would the standard error change if the sample size increased?
- Why is the standard error important in estimating the population mean?
- What role does sample size play in reducing the standard error?
- How would we interpret the standard error in the context of this experiment?
- What is the relationship between sample standard deviation and standard error?
Tip:
Increasing the sample size decreases the standard error, making the estimate of the population mean more precise.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Standard Error
Sampling
Formulas
Standard Error of the Mean (SEM) = s / √n
Theorems
Central Limit Theorem
Suitable Grade Level
Undergraduate Statistics
Related Recommendation
Calculate the Standard Error of the Mean for a Sample of 50 Employees
Standard Error Calculation with Finite Population Correction
Calculate Standard Error of the Mean with σ = 44 and Various Sample Sizes
How to Calculate the Standard Error of the Mean with a Sample Size of 40
Calculate Standard Error for a Sample Mean with σ = 21 and n = 49