From the side-by-side boxplots for the temperatures of males and females, do there seem to be any differences?Based on the 95% CI, is there gender difference in average body temperature? Explain.What is the estimated standard error of the sample mean difference? Have you made any assump- tion on population variances? Why is your variance assumption reasonable?Give a formal test for the difference in mean body temperature between males and females. Can the null hypothesis be rejected at level .05? At level .01? # Analysis of Temperature by Gender## 1. Box Plot AnalysisThe box plot displays the distribution of temperatures by gender, labeled as "F" for Female and "M" for Male. Key observations:- The temperature range for both genders appears similar, with most data points between 97°F and 100°F.- The median temperature for females seems slightly higher than for males.- Both box plots show outliers, evidenced by points outside the whiskers.## 2. Oneway ANOVA Analysis### Pooled t Test- **Difference**: -0.28923- **t Ratio**: -2.28543- **Standard Error of Difference (Std Err Dif)**: 0.12655- **Degrees of Freedom (DF)**: 128#### Confidence Levels- **Upper Confidence Limit (CL) Difference**: -0.03882- **Lower CL Difference**: -0.53964#### Probability Values- **Prob > |t|**: 0.0239 (significant at the 0.05 level)- **Prob > t**: 0.9880- **Prob < t**: 0.0120 (significant at the 0.05 level)- A significance is indicated by an asterisk (*) next to probability values.### T Distribution GraphThe graph visualizes the t distribution, highlighting the critical regions with a shaded area. The observed t value is marked on the distribution curve.## 3. Means for Oneway ANOVA- **Females (F)** - Number: 65 - Mean: 98.3938 - Standard Error: 0.08949 - 95% Confidence Interval: [98.217, 98.571]- **Males (M)** - Number: 65 - Mean: 98.1046 - Standard Error: 0.08949 - 95% Confidence Interval: [97.928, 98.282]The standard error uses a pooled estimate of error variance.## 4. Means and Standard Deviations- **Females (F)** - Number: 65 - Mean: 98.393846 - Standard Deviation: 0.7434878 - Standard Error Mean: 0.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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From the side-by-side boxplots for the temperatures of males and females, do there seem to be any differences?
Based on the 95% CI, is there gender difference in average body temperature? Explain.
What is the estimated standard error of the sample mean difference? Have you made any assump- tion on population variances? Why is your variance assumption reasonable?
Give a formal test for the difference in mean body temperature between males and females. Can the null hypothesis be rejected at level .05? At level .01?

# Analysis of Temperature by Gender

## 1. Box Plot Analysis
The box plot displays the distribution of temperatures by gender, labeled as "F" for Female and "M" for Male. Key observations:

- The temperature range for both genders appears similar, with most data points between 97°F and 100°F.
- The median temperature for females seems slightly higher than for males.
- Both box plots show outliers, evidenced by points outside the whiskers.

## 2. Oneway ANOVA Analysis

### Pooled t Test
- **Difference**: -0.28923
- **t Ratio**: -2.28543
- **Standard Error of Difference (Std Err Dif)**: 0.12655
- **Degrees of Freedom (DF)**: 128

#### Confidence Levels
- **Upper Confidence Limit (CL) Difference**: -0.03882
- **Lower CL Difference**: -0.53964

#### Probability Values
- **Prob > |t|**: 0.0239 (significant at the 0.05 level)
- **Prob > t**: 0.9880
- **Prob < t**: 0.0120 (significant at the 0.05 level)
- A significance is indicated by an asterisk (*) next to probability values.

### T Distribution Graph
The graph visualizes the t distribution, highlighting the critical regions with a shaded area. The observed t value is marked on the distribution curve.

## 3. Means for Oneway ANOVA
- **Females (F)**
- Number: 65
- Mean: 98.3938
- Standard Error: 0.08949
- 95% Confidence Interval: [98.217, 98.571]

- **Males (M)**
- Number: 65
- Mean: 98.1046
- Standard Error: 0.08949
- 95% Confidence Interval: [97.928, 98.282]

The standard error uses a pooled estimate of error variance.

## 4. Means and Standard Deviations

- **Females (F)**
- Number: 65
- Mean: 98.393846
- Standard Deviation: 0.7434878
- Standard Error Mean: 0.

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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