Test the claim below about the mean of the differences for a population of paired data at the level of significance a.Assume the samples are random and dependent, and the populations are normally distributed **Paired Data Hypothesis Test****Problem Statement:**Test the claim about the mean of the differences for a population of paired data at the level of significance, α. Assume the samples are random and dependent, and the populations are normally distributed.**Claim:** μₒ < 0; α = 0.05. **Sample Statistics:**- \( \bar{d} = 1.7 \)- \( s_d = 3.8 \)- \( n = 17 \)**Task:**Identify the null and alternative hypotheses. Choose the correct answer below.**Options:**- **A.** \( H_0: \mu_d \ge 0 \) \( H_a: \mu_d < 0 \) (Selected as correct) - **B.** \( H_0: \mu_d \le 0 \) \( H_a: \mu_d > 0 \) - **C.** \( H_0: \mu_d > 0 \) \( H_a: \mu_d \le 0 \) - **D.** \( H_0: \mu_d = 0 \) \( H_a: \mu_d \neq 0 \) - **E.** \( H_0: \mu_d < 0 \) \( H_a: \mu_d \ge 0 \) - **F.** \( H_0: \mu_d \neq 0 \) \( H_a: \mu_d = 0 \)**Result:**The test statistic is \( t = 1.84 \). (Round to two decimal places as needed.)**Further Step:**Determine the critical value(s), \( t_0 \). (Round to two decimal places as needed. Use a comma to separate answers as needed.)

Answered: Test the claim below about the mean of…

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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Test the claim below about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed

**Paired Data Hypothesis Test**

**Problem Statement:**
Test the claim about the mean of the differences for a population of paired data at the level of significance, α. Assume the samples are random and dependent, and the populations are normally distributed.

**Claim:** μₒ < 0; α = 0.05.

**Sample Statistics:**
- \( \bar{d} = 1.7 \)
- \( s_d = 3.8 \)
- \( n = 17 \)

**Task:**
Identify the null and alternative hypotheses. Choose the correct answer below.

**Options:**
- **A.** \( H_0: \mu_d \ge 0 \)
\( H_a: \mu_d < 0 \) (Selected as correct)

- **B.** \( H_0: \mu_d \le 0 \)
\( H_a: \mu_d > 0 \)

- **C.** \( H_0: \mu_d > 0 \)
\( H_a: \mu_d \le 0 \)

- **D.** \( H_0: \mu_d = 0 \)
\( H_a: \mu_d \neq 0 \)

- **E.** \( H_0: \mu_d < 0 \)
\( H_a: \mu_d \ge 0 \)

- **F.** \( H_0: \mu_d \neq 0 \)
\( H_a: \mu_d = 0 \)

**Result:**
The test statistic is \( t = 1.84 \).
(Round to two decimal places as needed.)

**Further Step:**
Determine the critical value(s), \( t_0 \).
(Round to two decimal places as needed. Use a comma to separate answers as needed.)

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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