ANSUR II 2012 ANSUR I 1988Here is the numbers:67.5 78.590.9 80.495.4 90.2103.7 78.679.1 72.177.3 85.5112.4 87.994.9 102.284.7 86.768.4 66.385.8 67.2105.4 88.085.192.0104.2 **Educational Resource: Statistical Hypothesis Testing****Objective:**We aim to test the claim that the mean weight of U.S. Army male personnel in 1988 is less than the mean weight in 2012. The data are based on independent random samples from two separate years: 1988 and 2012.**Procedure:**- Significance Level: 0.01- Population 1: 1988 weights- Population 2: 2012 weights**Hypotheses:**1. **Null Hypothesis (H₀)**: - Statement: The mean weight in 1988 (μ₁) is equal to the mean weight in 2012 (μ₂). - Notation: H₀: μ₁ = μ₂2. **Alternative Hypothesis (H₁)**: - Statement: The mean weight in 1988 (μ₁) is less than the mean weight in 2012 (μ₂). - Notation: H₁: μ₁ < μ₂**Options for Hypotheses Selection:**- **Option A:** - H₀: μ₁ = μ₂ - H₁: μ₁ < μ₂- **Option B:** - H₀: μ₁ < μ₂ - H₁: μ₁ ≥ μ₂- **Option C:** - H₀: μ₁ ≠ μ₂ - H₁: μ₁ = μ₂- **Option D:** - H₀: μ₁ = μ₂ - H₁: μ₁ ≠ μ₂**Conclusion:**For testing the claim that the 1988 mean weight is less than the 2012 mean weight using a significance level of 0.01, choose **Option A**. **Note:** Click the icon to view the detailed ANSUR data.This analysis assumes normal distribution for both populations and does not assume equal population standard deviations. The test statistic: □ (Round to two decimal places as needed.)The P-value is: □ (Round to three decimal places as needed.)State the conclusion for the test:A. Reject the null hypothesis. There is sufficient evidence to support the claim that the mean weight of the 1958 population is less than the mean weight of the 2012 population.B. Reject the null hypothesis. There is not sufficient evidence to support the claim that the mean weight of the 1958 population is less than the mean weight of the 2012 population.C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the mean weight of the 1958 population is less than the mean weight of the 2012 population.D. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the mean weight of the 1958 population is less than the mean weight of the 2012 population.b. Construct a confidence interval appropriate for this hypothesis test in part (a):□ < μ1 - μ2 < □ (Round to one decimal place as needed.)

Answered: Image /qna-images/answer/80c317e2-0c30-4b2c-ae49-8d7f5666617f.jpg

Answered: Here is the numbers: 67.5 78.5 90.9…

Here is the numbers: 67.5 78.5 90.9 80.4 95.4 90.2 103.7 78.6 79.1 72.1 77.3 85.5 112.4 87.9 94.9 102.2 84.7 86.7 68.4 66.3 85.8 67.2 105.4 88.0 85.1 92.0 104.2

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

ANSUR II 2012 ANSUR I 1988

Here is the numbers:

67.5 78.5
90.9 80.4
95.4 90.2
103.7 78.6
79.1 72.1
77.3 85.5
112.4 87.9
94.9 102.2
84.7 86.7
68.4 66.3
85.8 67.2
105.4 88.0
85.1
92.0
104.2

**Educational Resource: Statistical Hypothesis Testing**

**Objective:**
We aim to test the claim that the mean weight of U.S. Army male personnel in 1988 is less than the mean weight in 2012. The data are based on independent random samples from two separate years: 1988 and 2012.

**Procedure:**
- Significance Level: 0.01
- Population 1: 1988 weights
- Population 2: 2012 weights

**Hypotheses:**

1. **Null Hypothesis (H₀)**:
- Statement: The mean weight in 1988 (μ₁) is equal to the mean weight in 2012 (μ₂).
- Notation: H₀: μ₁ = μ₂

2. **Alternative Hypothesis (H₁)**:
- Statement: The mean weight in 1988 (μ₁) is less than the mean weight in 2012 (μ₂).
- Notation: H₁: μ₁ < μ₂

**Options for Hypotheses Selection:**

- **Option A:**
- H₀: μ₁ = μ₂
- H₁: μ₁ < μ₂

- **Option B:**
- H₀: μ₁ < μ₂
- H₁: μ₁ ≥ μ₂

- **Option C:**
- H₀: μ₁ ≠ μ₂
- H₁: μ₁ = μ₂

- **Option D:**
- H₀: μ₁ = μ₂
- H₁: μ₁ ≠ μ₂

**Conclusion:**
For testing the claim that the 1988 mean weight is less than the 2012 mean weight using a significance level of 0.01, choose **Option A**.

**Note:**
Click the icon to view the detailed ANSUR data.

This analysis assumes normal distribution for both populations and does not assume equal population standard deviations.

The test statistic: □ (Round to two decimal places as needed.)

The P-value is: □ (Round to three decimal places as needed.)

State the conclusion for the test:

A. Reject the null hypothesis. There is sufficient evidence to support the claim that the mean weight of the 1958 population is less than the mean weight of the 2012 population.

B. Reject the null hypothesis. There is not sufficient evidence to support the claim that the mean weight of the 1958 population is less than the mean weight of the 2012 population.

C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the mean weight of the 1958 population is less than the mean weight of the 2012 population.

D. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the mean weight of the 1958 population is less than the mean weight of the 2012 population.

b. Construct a confidence interval appropriate for this hypothesis test in part (a):

□ < μ1 - μ2 < □ (Round to one decimal place as needed.)

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