The test statistic 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. a. Reject the null hypothesis.There is sufficient evidence to support the claim that mean of weight of the 1988 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 mean of weight of the 1988 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 mean of weight of the 1988 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 mean of weight of the 1988 population is less than the mean weight of the 2012 population. b. Construct a confidence interval appropriate for the hypothesis test in part (a). ____________ < μ1 - μ2 < _____________________ (Round to one decimal place as needed.) The accompanying table lists the weights (kg) of randomly selected U.S. Army male personnel measured in 1988 (from "ANSUR I 1988") and different weights (kg) of randomly selected U.S. Army male personnel measured in 2012 (from "ANSUR II 2012"). Assume the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) and (b).Click the icon to view the ANSUR data.---a. Use a 0.05 significance level to test the claim that the mean weight of the 1988 population is less than the mean weight of the 2012 population.What are the null and alternative hypotheses? Assume that population 1 consists of the 1988 weights and population 2 consists of the 2012 weights.- **A.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 < \mu_2 \)- **B.** \( H_0: \mu_1 \neq \mu_2 \) \( H_1: \mu_1 = \mu_2 \)- **C.** \( H_0: \mu_1 \leq \mu_2 \) \( H_1: \mu_1 > \mu_2 \)- **D.** \( H_0: \mu_1 = \mu_2 \) \( H_1: \mu_1 \neq \mu_2 \) ### Data Comparison from ANSUR Research StudiesThe table below displays values from two separate ANSUR research studies conducted in different years, with measurements from ANSUR II in 2012 and ANSUR I in 1988.| ANSUR II 2012 | ANSUR I 1988 ||---------------|-------------|| 70.9 | 86.4 || 109.8 | 70.4 || 96.4 | 68.7 || 80.2 | 83.7 || 68.4 | 66.3 || 89.7 | 62.1 || 97.1 | 69.6 || 99.2 | 71.1 || 76.0 | 76.9 || 92.0 | 74.2 || 45.9 | 71.5 || 85.2 | 64.9 || 92.0 | || 74.4 | || 94.1 | |### OverviewThis table presents a set of numerical values from two different datasets related to anthropometric measurements. These values can provide insights into changes in human physical attributes over time, valuable for fields such as ergonomics, health, and design.

Answered: Listed in the accompanying table are…

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

The test statistic 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.

a. Reject the null hypothesis.There is sufficient evidence to support the claim that mean of weight of the 1988 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 mean of weight of the 1988 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 mean of weight of the 1988 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 mean of weight of the 1988 population is less than the mean weight of the 2012 population.

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

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

The accompanying table lists the weights (kg) of randomly selected U.S. Army male personnel measured in 1988 (from "ANSUR I 1988") and different weights (kg) of randomly selected U.S. Army male personnel measured in 2012 (from "ANSUR II 2012"). Assume the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) and (b).

Click the icon to view the ANSUR data.

---

a. Use a 0.05 significance level to test the claim that the mean weight of the 1988 population is less than the mean weight of the 2012 population.

What are the null and alternative hypotheses? Assume that population 1 consists of the 1988 weights and population 2 consists of the 2012 weights.

- **A.** \( H_0: \mu_1 = \mu_2 \)
\( H_1: \mu_1 < \mu_2 \)

- **B.** \( H_0: \mu_1 \neq \mu_2 \)
\( H_1: \mu_1 = \mu_2 \)

- **C.** \( H_0: \mu_1 \leq \mu_2 \)
\( H_1: \mu_1 > \mu_2 \)

- **D.** \( H_0: \mu_1 = \mu_2 \)
\( H_1: \mu_1 \neq \mu_2 \)

### Data Comparison from ANSUR Research Studies

The table below displays values from two separate ANSUR research studies conducted in different years, with measurements from ANSUR II in 2012 and ANSUR I in 1988.

| ANSUR II 2012 | ANSUR I 1988 |
|---------------|-------------|
| 70.9 | 86.4 |
| 109.8 | 70.4 |
| 96.4 | 68.7 |
| 80.2 | 83.7 |
| 68.4 | 66.3 |
| 89.7 | 62.1 |
| 97.1 | 69.6 |
| 99.2 | 71.1 |
| 76.0 | 76.9 |
| 92.0 | 74.2 |
| 45.9 | 71.5 |
| 85.2 | 64.9 |
| 92.0 | |
| 74.4 | |
| 94.1 | |

### Overview

This table presents a set of numerical values from two different datasets related to anthropometric measurements. These values can provide insights into changes in human physical attributes over time, valuable for fields such as ergonomics, health, and design.

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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