Answered: study was done on body temperatures of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.

a. The test statistic, t, is

(Round to two decimal places as needed.)

b. The P-value is

(Round to three decimal places as needed.)

c. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

less than mu 1 minus mu 2 less than

(Round to three decimal places as needed.)

This table compares temperature data between men and women. Here's the breakdown of the columns and rows:

### Table Data:

- **Columns:**
- Men
- Women

- **Rows:**
- μ: Mean temperature, denoted as \( \mu_1 \) for men and \( \mu_2 \) for women.
- n: Sample size
- 11 for men
- 59 for women
- \(\overline{x}\): Average temperature
- 97.64°F for men
- 97.25°F for women
- s: Standard deviation of temperature
- 0.88°F for men
- 0.69°F for women

This data is useful for analyzing the differences in mean body temperatures and their variances between men and women based on the samples provided.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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