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:

  1. **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:

  1. **Identify the sample **

    • We need the sample mean (xˉ\bar{x}), sample standard deviation (ss), and sample size (nn) for adult females.
  2. Determine the z-score (or t-score for small samples):

    • For a 90% confidence interval, the critical value zα/2z_{\alpha/2} 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).
  3. Apply the formula: The confidence interval formula is given by: xˉ±zα/2(sn)\bar{x} \pm z_{\alpha/2} \left(\frac{s}{\sqrt{n}}\right) where:

    • xˉ\bar{x} = sample mean
    • ss = sample standard deviation
    • nn = sample size
    • zα/2z_{\alpha/2} = 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