refer to the accompanying data set and construct a 90% confidence interval estimate of the mean pulse rate of adult males. Compare the results. The pulse rate for males in the data set are as follows. 86,77,50,60,52,61,54,78,49,64,74,62,66,77,84,63,67,96,45,86,72,65,72,71,51,64,54,78,72,64,63,93,57,67,57,59,70,72,86,55

To construct a 90% confidence interval estimate for the mean pulse rate of adult males based on the provided data set, we will follow these steps:

1. **Identify the Data**: The given pulse rates for adult males are:

   \( 86, 77, 50, 60, 52, 61, 54, 78, 49, 64, 74, 62, 66, 77, 84, 63, 67, 96, 45, 86, 72, 65, 72, 71, 51, 64, 54, 78, 72, 64, 63, 93, 57, 67, 57, 59, 70, 72, 86, 55 \).

2. **Calculate the Sample Mean (\(\bar{x}\))**: 
   This is the average pulse rate of the data set.

3. **Calculate the Sample Standard Deviation (\(s\))**: 
   This measures the spread or variability of the pulse rates.

4. **Determine the Sample Size (\(n\))**: 
   This is simply the number of pulse rates in the data set.

5. **Find the Appropriate z-value** for a 90% confidence level: 
   For a 90% confidence interval, the z-value is approximately 1.645.

6. **Calculate the Confidence Interval**:
   The confidence interval is given by the formula:
   \[
   \bar{x} \pm z \times \left(\frac{s}{\sqrt{n}}\right)
   \]
   Where:
   - \(\bar{x}\) is the sample mean,
   - \(z\) is the z-score for a 90% confidence interval (1.645),
   - \(s\) is the sample standard deviation,
   - \(n\) is the sample size.

Let me compute these values for you.### Results:
- **Sample Mean (\(\bar{x}\))**: 67.33
- **Sample Standard Deviation (\(s\))**: 12.40
- **Sample Size (\(n\))**: 40
- **90% Confidence Interval**: (64.10, 70.55)

This means we are 90% confident that the true mean pulse rate of adult males falls between **64.10** and **70.55** based on the given data.

Do you want further details or have any questions?

Here are 5 related questions you can consider:
1. What would happen to the confidence interval if we increased the sample size?
2. How would the confidence interval change with a different confidence level, such as 95%?
3. What is the interpretation of a confidence interval in this context?
4. How does the standard deviation influence the width of the confidence interval?
5. Could we use this method to compare the pulse rates of males versus females?

**Tip**: A larger sample size typically leads to a narrower confidence interval, increasing the precision of the estimate.

Refer to the accompanying data set and construct a 90% confidence interval estimate of the mean pulse rate of adult males. The pulse rate for males in the data set are as follows: 86, 77, 50, 60, 52, 61, 54, 78, 49, 64, 74, 62, 66, 77, 84, 63, 67, 96, 45, 86, 72, 65, 72, 71, 51, 64, 54, 78, 72, 64, 63, 93, 57, 67, 57, 59, 70, 72, 86, 55.

Learn how to construct a 90% confidence interval for the mean pulse rate of adult males using real data. This step-by-step guide covers statistical concepts such as the sample mean, sample standard deviation, and confidence interval calculations, providing a detailed example for Grades 10-12.

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