Math Problem Statement
Commute Times A random sample of 50 commuter students was taken to analyze how long it took them to drive to Babson on any given day. The SGA engaged a Business Analytics concentrator who created the following Minitab output. Use this output to answer the associated questions.
n = 50 mean = ? standard diviation = 29.18 95% confidence interval for μ = (36.93, 53.51)
Write out the 95% confidence interval for commute times. And write out a managerial conclusion in 30 words or less.
Solution
The 95% confidence interval for the mean commute time is between 36.93 minutes and 53.51 minutes.
Managerial Conclusion: We are 95% confident that the average commute time for Babson students falls between 36.93 and 53.51 minutes, which can aid in planning campus schedules and resource allocation.
Would you like further explanation on confidence intervals, or have other questions related to this?
- How do we calculate a confidence interval?
- What factors can affect the width of a confidence interval?
- Why is the sample size important in statistical analysis?
- How does the confidence level (e.g., 95%) impact results?
- How can businesses use commute time data for operational planning?
Tip: To narrow a confidence interval, increase the sample size, which reduces the margin of error.
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Math Problem Analysis
Mathematical Concepts
Confidence Intervals
Descriptive Statistics
Inferential Statistics
Formulas
Confidence Interval Formula for Mean: µ = x̄ ± Z * (σ/√n)
Theorems
Central Limit Theorem
Confidence Interval Theorem
Suitable Grade Level
Grades 11-13
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