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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 resu

To address your request, I'll first guide you through how to calculate the 90% confidence interval (CI) for the mean pulse rates of both adult females and males using the data from the image.

### Steps:
1. **Extract the Data**: 
   From the table shown in the image, we have the pulse rates for both males and females.

   - **Males' Pulse Rates**:
     - 86, 77, 60, 61, 64, 54, 48, 77, 86, 45
     - 72, 65, 71, 55, 81, 54, 58, 64, 77, 86
     
   - **Females' Pulse Rates**:
     - 77, 95, 85, 76, 84, 81, 79, 78, 95, 65
     - 81, 82, 72, 58, 81, 87, 84, 79, 75, 55

2. **Calculate the Mean**: For both males and females, calculate the sample mean pulse rate.
   
3. **Calculate the Standard Deviation**: Compute the standard deviation for each sample to understand the spread of the data.

4. **Determine the 90% Confidence Interval Formula**: Use the formula for the confidence interval:
   \[
   CI = \bar{x} \pm z \left(\frac{\sigma}{\sqrt{n}}\right)
   \]
   Where:
   - \(\bar{x}\) is the sample mean
   - \(z\) is the z-score for the confidence level (1.645 for 90%)
   - \(\sigma\) is the standard deviation
   - \(n\) is the sample size

5. **Calculate the Confidence Intervals**: For both genders, apply the formula to determine the 90% CI.

Let me calculate this for you.### Results:

- **Males**:
  - Mean Pulse Rate: 68.3 bpm
  - 90% Confidence Interval: (63.80, 72.80) bpm

- **Females**:
  - Mean Pulse Rate: 78.45 bpm
  - 90% Confidence Interval: (74.71, 82.19) bpm

### Comparison:
The mean pulse rate for females is higher than that for males, and the confidence intervals reflect this difference. While there is no overlap between the two intervals, the spread of the confidence intervals for both genders suggests a distinct difference in the average pulse rates.

Would you like further clarification on these calculations or any details?

### Follow-up Questions:
1. How would the confidence interval change with a different confidence level?
2. How does sample size affect the width of the confidence interval?
3. Why is it important to use the sample standard deviation rather than the population standard deviation in this case?
4. Could overlapping confidence intervals indicate similar pulse rates for males and females?
5. What might be the reason for the observed difference in mean pulse rates between males and females?

**Tip**: Increasing the sample size decreases the margin of error, leading to a more precise confidence interval.

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.

Learn how to calculate 90% confidence intervals for the mean pulse rates of adult females and males using statistical methods. This guide covers sample mean calculations, standard deviation, and confidence interval formulas.

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