Homework Help is Here – Start Your Trial Now!
Math
Statistics
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. Complete parts (a) and (b) below. a. Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women. What are the null and alternative hypotheses? A. Ho: H₁ H2 H₁: Hy > H₂ OC. Ho H1 242 H₁: Hy

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. Complete parts (a) and (b) below. a. Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women. What are the null and alternative hypotheses? A. Ho: H₁ H2 H₁: Hy > H₂ OC. Ho H1 242 H₁: Hy

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
See similar textbooks
icon
Related questions
Question
### Hypothesis Testing of Body Temperatures for Men and Women #### Study Overview and Data Description A 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 Testing Using 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 > μ₂ 2. **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
Transcribed Image Text:### Hypothesis Testing of Body Temperatures for Men and Women #### Study Overview and Data Description A 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 Testing Using 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 > μ₂ 2. **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
Expert Solution
steps

Step by step

Solved in 7 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
SEE MORE TEXTBOOKS