### Hypothesis Testing of Body Temperatures for Men and Women#### Study Overview and Data DescriptionA study was conducted to analyze body temperatures of men and women. The results are summarized in the table below. The study assumes that the data collected comes from two independent simple random samples from normally distributed populations. It does not assume equal population standard deviations.| Group | Mean (μ) | Sample Size (n) | Sample Mean (x̄) | Sample Standard Deviation (s) ||--------|-----------------|-----------------|------------------|-------------------------------|| Men | μ₁ (Mean₁) | 11 | 97.76°F | 0.89°F || Women | μ₂ (Mean₂) | 59 | 97.32°F | 0.63°F |#### Hypothesis TestingUsing a 0.01 significance level, we will test whether men have a higher mean body temperature than women. The steps are outlined below.1. **Formulate the Hypotheses:** - **Null Hypothesis (H₀):** μ₁ = μ₂ - **Alternative Hypothesis (H₁):** μ₁ > μ₂2. **Test Statistic:** - The test statistic, t, is calculated to be 1.57 (rounded to two decimal places as needed).3. **P-value:** - The P-value is calculated to be 0.071 (rounded to three decimal places as needed).4. **Conclusion Based on P-value:** - **Reject the null hypothesis:** There is sufficient evidence to support the claim that men have a higher mean body temperature than women. - **Fail to reject the null hypothesis:** There is not sufficient evidence to support the claim that men have a higher mean body temperature than women. Given the P-value of 0.071 is greater than the significance level of 0.01, we **fail to reject the null hypothesis**. Therefore, there is not sufficient evidence to support the claim that men have a higher mean body temperature than women.5. **Confidence Interval:** - Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women. - The calculated confidence interval is (-0.28, 1.16) (rounded to three decimal places as needed).#### Summary

Given: n1=11n2=59s1=0.89s2=0.63x¯1=97.76x¯2=97.32σ=0.01

Answered: A study was done on body temperatures…

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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