Sure, here's a transcription suitable for an educational website: --- **Hypothesis Testing: Comparing Two Means** **Problem Statement:** 5. Test the claim that \(\mu_1 = \mu_2\). Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that the variances are unknown with \(\sigma_1^2 \neq \sigma_2^2\). **Hypotheses:** - \(H_0: \mu_1 = \mu_2\) (Claim) - \(H_a: \mu_1 \neq \mu_2\) **Sample Data:** \[ \begin{array}{|c|c|c|} \hline & \text{Sample 1} & \text{Sample 2} \\ \hline n_1 = 37 & n_2 = 25 \\ \overline{x}_1 = 37.9 & \overline{x}_2 = 36.8 \\ s_1 = 1.5 & s_2 = 1.9 \\ \hline \end{array} \] Find the test statistic and critical values of the rejection region to help you make a conclusion. At \(\alpha = 0.05\), the claim \(H_0\) is: A. Not rejected because the test statistic 2.428 is not in the rejection region with critical values \(\pm2.0639\) B. Rejected because the test statistic 2.428 is in the rejection region with critical values \(\pm1.7109\) C. Rejected because the test statistic 2.542 is in the rejection region with critical values \(\pm1.7109\) D. Not rejected because the test statistic \(-2.542\) is not in the rejection region with critical values \(\pm1.7109\) E. Rejected because the test statistic 2.428 is in the rejection region with critical values \(\pm2.0639\) --- **Explanation of the Problem:** The question asks you to perform hypothesis testing to determine if there is a significant difference between the means of two independent samples. The variances are unknown and assumed to be unequal. You are given sample sizes, means, and standard deviations for both samples. Your task
Sure, here's a transcription suitable for an educational website: --- **Hypothesis Testing: Comparing Two Means** **Problem Statement:** 5. Test the claim that \(\mu_1 = \mu_2\). Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that the variances are unknown with \(\sigma_1^2 \neq \sigma_2^2\). **Hypotheses:** - \(H_0: \mu_1 = \mu_2\) (Claim) - \(H_a: \mu_1 \neq \mu_2\) **Sample Data:** \[ \begin{array}{|c|c|c|} \hline & \text{Sample 1} & \text{Sample 2} \\ \hline n_1 = 37 & n_2 = 25 \\ \overline{x}_1 = 37.9 & \overline{x}_2 = 36.8 \\ s_1 = 1.5 & s_2 = 1.9 \\ \hline \end{array} \] Find the test statistic and critical values of the rejection region to help you make a conclusion. At \(\alpha = 0.05\), the claim \(H_0\) is: A. Not rejected because the test statistic 2.428 is not in the rejection region with critical values \(\pm2.0639\) B. Rejected because the test statistic 2.428 is in the rejection region with critical values \(\pm1.7109\) C. Rejected because the test statistic 2.542 is in the rejection region with critical values \(\pm1.7109\) D. Not rejected because the test statistic \(-2.542\) is not in the rejection region with critical values \(\pm1.7109\) E. Rejected because the test statistic 2.428 is in the rejection region with critical values \(\pm2.0639\) --- **Explanation of the Problem:** The question asks you to perform hypothesis testing to determine if there is a significant difference between the means of two independent samples. The variances are unknown and assumed to be unequal. You are given sample sizes, means, and standard deviations for both samples. Your task
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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![Sure, here's a transcription suitable for an educational website:
---
**Hypothesis Testing: Comparing Two Means**
**Problem Statement:**
5. Test the claim that \(\mu_1 = \mu_2\). Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that the variances are unknown with \(\sigma_1^2 \neq \sigma_2^2\).
**Hypotheses:**
- \(H_0: \mu_1 = \mu_2\) (Claim)
- \(H_a: \mu_1 \neq \mu_2\)
**Sample Data:**
\[
\begin{array}{|c|c|c|}
\hline
& \text{Sample 1} & \text{Sample 2} \\
\hline
n_1 = 37 & n_2 = 25 \\
\overline{x}_1 = 37.9 & \overline{x}_2 = 36.8 \\
s_1 = 1.5 & s_2 = 1.9 \\
\hline
\end{array}
\]
Find the test statistic and critical values of the rejection region to help you make a conclusion.
At \(\alpha = 0.05\), the claim \(H_0\) is:
A. Not rejected because the test statistic 2.428 is not in the rejection region with critical values \(\pm2.0639\)
B. Rejected because the test statistic 2.428 is in the rejection region with critical values \(\pm1.7109\)
C. Rejected because the test statistic 2.542 is in the rejection region with critical values \(\pm1.7109\)
D. Not rejected because the test statistic \(-2.542\) is not in the rejection region with critical values \(\pm1.7109\)
E. Rejected because the test statistic 2.428 is in the rejection region with critical values \(\pm2.0639\)
---
**Explanation of the Problem:**
The question asks you to perform hypothesis testing to determine if there is a significant difference between the means of two independent samples. The variances are unknown and assumed to be unequal. You are given sample sizes, means, and standard deviations for both samples. Your task](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa39be845-ae1d-44f6-957a-0c42c0fe4c23%2F4c3928e7-92be-4141-a73c-e654fcaeb864%2Fji5yytr.jpeg&w=3840&q=75)
Transcribed Image Text:Sure, here's a transcription suitable for an educational website:
---
**Hypothesis Testing: Comparing Two Means**
**Problem Statement:**
5. Test the claim that \(\mu_1 = \mu_2\). Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that the variances are unknown with \(\sigma_1^2 \neq \sigma_2^2\).
**Hypotheses:**
- \(H_0: \mu_1 = \mu_2\) (Claim)
- \(H_a: \mu_1 \neq \mu_2\)
**Sample Data:**
\[
\begin{array}{|c|c|c|}
\hline
& \text{Sample 1} & \text{Sample 2} \\
\hline
n_1 = 37 & n_2 = 25 \\
\overline{x}_1 = 37.9 & \overline{x}_2 = 36.8 \\
s_1 = 1.5 & s_2 = 1.9 \\
\hline
\end{array}
\]
Find the test statistic and critical values of the rejection region to help you make a conclusion.
At \(\alpha = 0.05\), the claim \(H_0\) is:
A. Not rejected because the test statistic 2.428 is not in the rejection region with critical values \(\pm2.0639\)
B. Rejected because the test statistic 2.428 is in the rejection region with critical values \(\pm1.7109\)
C. Rejected because the test statistic 2.542 is in the rejection region with critical values \(\pm1.7109\)
D. Not rejected because the test statistic \(-2.542\) is not in the rejection region with critical values \(\pm1.7109\)
E. Rejected because the test statistic 2.428 is in the rejection region with critical values \(\pm2.0639\)
---
**Explanation of the Problem:**
The question asks you to perform hypothesis testing to determine if there is a significant difference between the means of two independent samples. The variances are unknown and assumed to be unequal. You are given sample sizes, means, and standard deviations for both samples. Your task
Expert Solution
Step 1
Given Data :
Null and Alternate Hypothesis :
Population variances are unequal
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