Math Problem Statement
Refer to the accompanying data set and construct a 90% confidence interval estimate of the mean pulse rate of adult females; then do the same for adult males. Compare the results. LOADING... Click the icon to view the pulse rates for adult females and adult males. Question content area bottom Part 1 Construct a 90% confidence interval of the mean pulse rate for adult females.
72.2 bpmless thanmuless than
76.4 bpm (Round to one decimal place as needed.)
Solution
To construct a 90% confidence interval for the mean pulse rate of adult females, we follow these steps:
Steps for Confidence Interval Calculation:
- **Identify the sample dataTo construct a 90% confidence interval for the mean pulse rate of adult females, we follow these steps:
Steps for Confidence Interval Calculation:
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**Identify the sample **
- We need the sample mean (), sample standard deviation (), and sample size () for adult females.
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Determine the z-score (or t-score for small samples):
- For a 90% confidence interval, the critical value corresponds to the 5th percentile in a standard normal distribution, which is approximately 1.645 (since 90% confidence interval splits the remaining 10% into 5% in each tail).
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Apply the formula: The confidence interval formula is given by: where:
- = sample mean
- = sample standard deviation
- = sample size
- = critical value from z-distribution for a 90% confidence
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Normal Distribution
Formulas
Confidence Interval formula: CI = x̄ ± z(α/2) * (σ/√n)
Standard Error formula: SE = σ/√n
Theorems
Central Limit Theorem
Normal Approximation
Suitable Grade Level
Grades 11-12
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