Tests the claim that . Assume the samples are normally distributed, random and independent. of = o 0.57; $2= = 0.66 = 45.14; 44.85 n= 20; ng = 19 %3D a. Calculate the Standard Error s-= (use 3 decimals) b. Calculate the t-test statistic using the standard error from part a.t = (use 2 decimal places) m? df
Tests the claim that . Assume the samples are normally distributed, random and independent. of = o 0.57; $2= = 0.66 = 45.14; 44.85 n= 20; ng = 19 %3D a. Calculate the Standard Error s-= (use 3 decimals) b. Calculate the t-test statistic using the standard error from part a.t = (use 2 decimal places) m? df
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
![**Testing the Claim That \( \mu_1 \neq \mu_2 \)**
Assume the samples are normally distributed, random, and independent.
\[
\sigma_1^2 = \sigma_2^2
\]
\[
s_1 = 0.57; \quad s_2 = 0.66
\]
\[
\bar{x}_1 = 45.14; \quad \bar{x}_2 = 44.85
\]
\[
n_1 = 20; \quad n_2 = 19
\]
a. **Calculate the Standard Error \( s_{\bar{x}_1 - \bar{x}_2} \):**
\(\boxed{\phantom{0.000}}\) (use 3 decimals)
b. **Calculate the t-test statistic using the standard error from part a.**
\( t = \boxed{\phantom{0.00}} \) (use 2 decimal places)
c. **What are the degrees of freedom?**
\( df = \boxed{\phantom{0}} \)
d. **At \( \alpha = 0.01 \), use the distribution table to find the critical values for the rejection region.**
\( t_c = \pm \boxed{\phantom{0.0000}} \) (use 4 decimal places)
e. **What is your conclusion?**
- \( \bigcirc \) Accept the alternative hypothesis and reject the claim
- \( \bigcirc \) Accept the null hypothesis and support the claim
- \( \bigcirc \) Reject the null hypothesis and support the claim
- \( \bigcirc \) Fail to reject the null hypothesis and do not support the claim
- \( \bigcirc \) Reject the alternative hypothesis and support the claim](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa86a1608-4622-4bb5-9da8-5fb01306e299%2Fb34165d6-0d73-480c-9d87-4de842141327%2Fgfco6m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Testing the Claim That \( \mu_1 \neq \mu_2 \)**
Assume the samples are normally distributed, random, and independent.
\[
\sigma_1^2 = \sigma_2^2
\]
\[
s_1 = 0.57; \quad s_2 = 0.66
\]
\[
\bar{x}_1 = 45.14; \quad \bar{x}_2 = 44.85
\]
\[
n_1 = 20; \quad n_2 = 19
\]
a. **Calculate the Standard Error \( s_{\bar{x}_1 - \bar{x}_2} \):**
\(\boxed{\phantom{0.000}}\) (use 3 decimals)
b. **Calculate the t-test statistic using the standard error from part a.**
\( t = \boxed{\phantom{0.00}} \) (use 2 decimal places)
c. **What are the degrees of freedom?**
\( df = \boxed{\phantom{0}} \)
d. **At \( \alpha = 0.01 \), use the distribution table to find the critical values for the rejection region.**
\( t_c = \pm \boxed{\phantom{0.0000}} \) (use 4 decimal places)
e. **What is your conclusion?**
- \( \bigcirc \) Accept the alternative hypothesis and reject the claim
- \( \bigcirc \) Accept the null hypothesis and support the claim
- \( \bigcirc \) Reject the null hypothesis and support the claim
- \( \bigcirc \) Fail to reject the null hypothesis and do not support the claim
- \( \bigcirc \) Reject the alternative hypothesis and support the claim
Expert Solution
Step 1
Given Data :
For Sample 1
x̄1 = 45.14
s1 = 0.57
n1 = 20
For Sample 2
x̄2 = 44.85
s2 = 0.66
n2 = 19
Significance level, α= 0.01
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