Given in the table are the BMI statistics for random samples of men and women. 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. Use a 0.01 significance level for both parts. a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? OA. H₂: H₁ H₂ H₁ H₁ H₂ OC. H₂: H₁ H₂ H₁: ₁₂ The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. OB. Ho: ₁2₂ H₁: #₁ #₂ <1₁-₂< (Round to three decimal places as needed.) Does the confidence interval support the conclusion of the test? because the confidence interval contains OD. Ho: H₁ H₁: #₁ OA. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. OB. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. OC. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. OD. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI. H₂ #₂ H P₁ n 41 x 27.8361 s 8.615006 H₂ 41 25.2703 4.560128
Given in the table are the BMI statistics for random samples of men and women. 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. Use a 0.01 significance level for both parts. a. Test the claim that males and females have the same mean body mass index (BMI). What are the null and alternative hypotheses? OA. H₂: H₁ H₂ H₁ H₁ H₂ OC. H₂: H₁ H₂ H₁: ₁₂ The test statistic, t, is (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) State the conclusion for the test. OB. Ho: ₁2₂ H₁: #₁ #₂ <1₁-₂< (Round to three decimal places as needed.) Does the confidence interval support the conclusion of the test? because the confidence interval contains OD. Ho: H₁ H₁: #₁ OA. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. OB. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. OC. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. OD. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI. b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI. H₂ #₂ H P₁ n 41 x 27.8361 s 8.615006 H₂ 41 25.2703 4.560128
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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![### Analysis of BMI Statistics for Men and Women
Given are the BMI statistics for random samples of men and women. These samples are independent, derived from normally distributed populations. Assume no equality in population standard deviations. A 0.01 significance level is used for the analysis below.
#### a. Testing the Hypothesis for Mean BMI Equality Between Genders
**Objective:** Test the claim that males and females have the same mean body mass index (BMI).
**Hypotheses:**
- Null Hypothesis (H₀): μ₁ = μ₂ (The mean BMI for men and women is equal.)
- Alternative Hypotheses:
- A. H₀: μ₁ = μ₂, H₁: μ₁ ≠ μ₂
- B. H₀: μ₁ ≤ μ₂, H₁: μ₁ > μ₂
- C. H₀: μ₁ ≥ μ₂, H₁: μ₁ < μ₂
- D. H₀: μ₁ ≠ μ₂, H₁: μ₁ = μ₂
**Test Statistic (t):** To be calculated and rounded to two decimal places.
**P-value:** To be calculated and rounded to three decimal places.
**Conclusion Options:**
- A. Fail to reject the null hypothesis. Sufficient evidence warrants no rejection.
- B. Fail to reject the null hypothesis. Insufficient evidence warrants rejection.
- C. Reject the null hypothesis. Sufficient evidence warrants rejection.
- D. Reject the null hypothesis. Insufficient evidence to claim equality.
#### b. Constructing the Confidence Interval
Construct a confidence interval to test if men and women have the same mean BMI.
- \[ \langle \mu_1 - \mu_2 \rangle \] (Fill in the values and round to three decimal places.)
**Support for Conclusion:**
The confidence interval will indicate whether it supports the hypothesis test outcome:
- Choose based on whether the confidence interval includes zero.
#### Data Summary (Table)
**Statistics Provided:**
- Sample size (\( n \)): 41 for both males and females
- Mean (\( \bar{x} \)):
- Males: 27.8361
- Females: 25.2703
- Standard deviation (\( s \)):
- Males: 8.615006](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F380d9f31-f164-4bec-9918-398c63ccd8d5%2Fa9a889ec-d9ed-46f2-9c29-2a817df07bca%2Fgqxcdsl_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of BMI Statistics for Men and Women
Given are the BMI statistics for random samples of men and women. These samples are independent, derived from normally distributed populations. Assume no equality in population standard deviations. A 0.01 significance level is used for the analysis below.
#### a. Testing the Hypothesis for Mean BMI Equality Between Genders
**Objective:** Test the claim that males and females have the same mean body mass index (BMI).
**Hypotheses:**
- Null Hypothesis (H₀): μ₁ = μ₂ (The mean BMI for men and women is equal.)
- Alternative Hypotheses:
- A. H₀: μ₁ = μ₂, H₁: μ₁ ≠ μ₂
- B. H₀: μ₁ ≤ μ₂, H₁: μ₁ > μ₂
- C. H₀: μ₁ ≥ μ₂, H₁: μ₁ < μ₂
- D. H₀: μ₁ ≠ μ₂, H₁: μ₁ = μ₂
**Test Statistic (t):** To be calculated and rounded to two decimal places.
**P-value:** To be calculated and rounded to three decimal places.
**Conclusion Options:**
- A. Fail to reject the null hypothesis. Sufficient evidence warrants no rejection.
- B. Fail to reject the null hypothesis. Insufficient evidence warrants rejection.
- C. Reject the null hypothesis. Sufficient evidence warrants rejection.
- D. Reject the null hypothesis. Insufficient evidence to claim equality.
#### b. Constructing the Confidence Interval
Construct a confidence interval to test if men and women have the same mean BMI.
- \[ \langle \mu_1 - \mu_2 \rangle \] (Fill in the values and round to three decimal places.)
**Support for Conclusion:**
The confidence interval will indicate whether it supports the hypothesis test outcome:
- Choose based on whether the confidence interval includes zero.
#### Data Summary (Table)
**Statistics Provided:**
- Sample size (\( n \)): 41 for both males and females
- Mean (\( \bar{x} \)):
- Males: 27.8361
- Females: 25.2703
- Standard deviation (\( s \)):
- Males: 8.615006
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