Math Problem Statement
The lifetime of a certain type of battery is known to be normally distributed with standard deviation o = 17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery. What is the standard error?
Solution
To calculate the standard error (SE) of the sample mean, use the formula:
Where:
- hours (the population standard deviation),
- (the sample size).
Step-by-Step Calculation:
Final Answer:
The standard error (SE) is approximately 2.404 hours.
Would you like assistance calculating the confidence interval or more explanation? Here are 5 related questions to expand:
- How is the confidence interval constructed for a population mean?
- Why is the standard error important in statistical inference?
- What is the z-score for a 95% confidence interval, and how is it applied?
- How would the sample size affect the width of the confidence interval?
- How does the assumption of normality influence this calculation?
Tip: For normally distributed data, knowing the standard deviation helps directly compute the standard error and confidence intervals effectively!
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Standard Error
Formulas
SE = σ / √n
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 10-12
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