Math Problem Statement

Refer to the accompanying data set and construct a

9595​%

confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.

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Part 1

Construct a

9595​%

confidence interval of the mean pulse rate for adult females.

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bpmless than<muμless than<enter your response here

bpm

​(Round to one decimal place as​ needed.)

Solution

To construct a 95% confidence interval for the mean pulse rate for adult females, I need to calculate the sample mean, sample standard deviation, and margin of error based on the given data. I'll proceed with these steps:

  1. Calculate the sample mean (xˉ\bar{x}) for adult females.
  2. Calculate the sample standard deviation (s) for adult females.
  3. Calculate the standard error of the mean (SEM), which is SEM=sn\text{SEM} = \frac{s}{\sqrt{n}}, where nn is the sample size.
  4. Determine the margin of error (ME) using the z-score for a 95% confidence level, which is 1.96 (for a normal distribution).
  5. Construct the confidence interval (CI) using the formula: CI=xˉ±(z-score×SEM)\text{CI} = \bar{x} \pm (\text{z-score} \times \text{SEM})

If you provide the data for pulse rates, I can perform these calculations directly, or you can let me know if you need more guidance on any specific step.

Let me know if you would like details on these steps or if you have questions on specific calculations.


Relative Questions:

  1. How would you interpret a confidence interval in the context of pulse rates?
  2. What does a 95% confidence interval signify in medical research?
  3. How might the results vary if a different confidence level was chosen, like 90% or 99%?
  4. What assumptions are required to use the z-score for this confidence interval?
  5. Why is it important to compare male and female pulse rates?

Tip:

Always check if the sample size is large enough to approximate the population's normality when using confidence intervals.

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Interval
Normal Distribution

Formulas

Sample Mean (x̄) = Σx / n
Sample Standard Deviation (s) = sqrt(Σ(x - x̄)² / (n - 1))
Standard Error (SEM) = s / sqrt(n)
Confidence Interval (CI) = x̄ ± (z * SEM)

Theorems

Central Limit Theorem

Suitable Grade Level

College Level Statistics