MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Title: Confidence Interval Estimation of Mean Body Temperature**

A data set includes 104 body temperatures of healthy adult humans, having a mean of 98.7°F and a standard deviation of 0.66°F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body temperature?

- Click here to view a t distribution table.
- Click here to view page 1 of the standard normal distribution table.
- Click here to view page 2 of the standard normal distribution table.

---

**What is the confidence interval estimate of the population mean μ?**

\[ \_\_\_ °F < μ < \_\_\_ °F \]

(Round to three decimal places as needed.)

**What does this suggest about the use of 98.6°F as the mean body temperature?**

- A. This suggests that the mean body temperature is lower than 98.6°F.
- B. This suggests that the mean body temperature is higher than 98.6°F.
- C. This suggests that the mean body temperature could very possibly be 98.6°F.

---

*Note: This section is aimed at helping students understand statistical concepts related to confidence intervals and their implications on interpreting mean values in a population.*
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Transcribed Image Text:**Title: Confidence Interval Estimation of Mean Body Temperature** A data set includes 104 body temperatures of healthy adult humans, having a mean of 98.7°F and a standard deviation of 0.66°F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body temperature? - Click here to view a t distribution table. - Click here to view page 1 of the standard normal distribution table. - Click here to view page 2 of the standard normal distribution table. --- **What is the confidence interval estimate of the population mean μ?** \[ \_\_\_ °F < μ < \_\_\_ °F \] (Round to three decimal places as needed.) **What does this suggest about the use of 98.6°F as the mean body temperature?** - A. This suggests that the mean body temperature is lower than 98.6°F. - B. This suggests that the mean body temperature is higher than 98.6°F. - C. This suggests that the mean body temperature could very possibly be 98.6°F. --- *Note: This section is aimed at helping students understand statistical concepts related to confidence intervals and their implications on interpreting mean values in a population.*
**POSITIVE z Scores: Cumulative Area from the LEFT**

This table shows the cumulative area from the left under a standard normal distribution curve for positive z-scores, indicating the probability of a standard normal random variable being less than a specific z value.

**Table Layout:**
- **Top row**: Displays the hundredths digit (.00, .01, ..., .09).
- **First column**: Displays the tenths digit of z (0.0 to 3.4).

**Table Data:**
The table provides cumulative probabilities for z-scores from 0.00 to 3.49. For example:
- A z-score of 0.0 has a cumulative area of 0.5000.
- A z-score of 1.0 has a cumulative area of 0.8413.
- A z-score of 2.3 has a cumulative area of 0.9893.

Values increase as z increases, showing the cumulative probability of a random variable falling below that z-score.

**Graph Explanation:**
Above the table, there's a bell-shaped curve representing a standard normal distribution centered at 0. The highlighted area to the left of a positive z value indicates the cumulative probability.

**Note:**
For z-scores of 3.50 or higher, use 0.9999 for the area.

**Common Critical Values:**
- .01 (z = 2.33)
- .05 (z = 1.645)
- .10 (z = 1.282)
- .50 (z = 0.0)

The table is essential for statistical analysis, particularly in determining probabilities related to the normal distribution.
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Transcribed Image Text:**POSITIVE z Scores: Cumulative Area from the LEFT** This table shows the cumulative area from the left under a standard normal distribution curve for positive z-scores, indicating the probability of a standard normal random variable being less than a specific z value. **Table Layout:** - **Top row**: Displays the hundredths digit (.00, .01, ..., .09). - **First column**: Displays the tenths digit of z (0.0 to 3.4). **Table Data:** The table provides cumulative probabilities for z-scores from 0.00 to 3.49. For example: - A z-score of 0.0 has a cumulative area of 0.5000. - A z-score of 1.0 has a cumulative area of 0.8413. - A z-score of 2.3 has a cumulative area of 0.9893. Values increase as z increases, showing the cumulative probability of a random variable falling below that z-score. **Graph Explanation:** Above the table, there's a bell-shaped curve representing a standard normal distribution centered at 0. The highlighted area to the left of a positive z value indicates the cumulative probability. **Note:** For z-scores of 3.50 or higher, use 0.9999 for the area. **Common Critical Values:** - .01 (z = 2.33) - .05 (z = 1.645) - .10 (z = 1.282) - .50 (z = 0.0) The table is essential for statistical analysis, particularly in determining probabilities related to the normal distribution.
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