Subiect Is achieving a basic skill level related to the location of the school? The results of a random sample of students by the location of school and the number of students achieving basic skill levels in three subjects is shown in the contingency table. At a=0.10, test the hypothesis that the variables are independent. Complete parts (a) through (d). Location Reading Math Science Urban Suburban 62 60 89 (a) Identify the claim and state the null and alternative hypotheses. Ha: Skill level in a subject is (1). location H Skill level in a subject is (2) location The (3) is the claim (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? df = Find the critical value (Round to three decimal places as needed.) Choose the correct rejection region below. OB. 7>r OD. sr (c) Calculate the test statistic. If comvenient, use technology (Round to three decimal places as needed) (d) Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. Choose the correct conclusion below. O A. Reject the nul hypothesis. There is not enough evidence to reject the claim that skill level in a subject is independent of location OC. Fail to reject the null hypothesis. There is not enough evidence to reject the claim that skill level in a subject is independent of location. O B. Fail to reject the nul hypothesis. There is enough evidence to reject the claim that skill level in a subject is independent of location. OD. Reject the null hypothesis. There is enough evidence to reject the claim that skill level in a subject is independent of location. (1) O dependent on (2) O dependent on (3) O alternative hypothesis O ndependent of O hndependent of O null hypothesis
Subiect Is achieving a basic skill level related to the location of the school? The results of a random sample of students by the location of school and the number of students achieving basic skill levels in three subjects is shown in the contingency table. At a=0.10, test the hypothesis that the variables are independent. Complete parts (a) through (d). Location Reading Math Science Urban Suburban 62 60 89 (a) Identify the claim and state the null and alternative hypotheses. Ha: Skill level in a subject is (1). location H Skill level in a subject is (2) location The (3) is the claim (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? df = Find the critical value (Round to three decimal places as needed.) Choose the correct rejection region below. OB. 7>r OD. sr (c) Calculate the test statistic. If comvenient, use technology (Round to three decimal places as needed) (d) Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. Choose the correct conclusion below. O A. Reject the nul hypothesis. There is not enough evidence to reject the claim that skill level in a subject is independent of location OC. Fail to reject the null hypothesis. There is not enough evidence to reject the claim that skill level in a subject is independent of location. O B. Fail to reject the nul hypothesis. There is enough evidence to reject the claim that skill level in a subject is independent of location. OD. Reject the null hypothesis. There is enough evidence to reject the claim that skill level in a subject is independent of location. (1) O dependent on (2) O dependent on (3) O alternative hypothesis O ndependent of O hndependent of O null hypothesis
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Topic Video
Question
![### Hypothesis Test: Relationship Between Skill Level and School Location
#### Problem Statement
Is achieving a basic skill level related to the location of the school? A random sample of students was surveyed, and their skill levels in three subjects (Reading, Math, Science) are shown in the contingency table below. At a significance level of α = 0.10, test the hypothesis that the variables are independent.
#### Contingency Table
| Location | Reading | Math | Science |
|-----------|---------|------|---------|
| Urban | 48 | 47 | 39 |
| Suburban | 62 | 60 | 69 |
#### Steps to Test Hypothesis
##### (a) Identify the Claim and State the Null and Alternative Hypotheses
- **Null Hypothesis (H₀):** Skill level in a subject is independent of location.
- **Alternative Hypothesis (H₁):** Skill level in a subject is dependent on location.
- **Claim:** (3) The claim is the alternative hypothesis.
##### (b) Determine the Degrees of Freedom, Find the Critical Value, and Identify the Rejection Region
1. **Degrees of Freedom (d.f.):**
\[
(\text{Number of rows} - 1) \times (\text{Number of columns} - 1) = (2 - 1) \times (3 - 1) = 2
\]
2. **Find the Critical Value:**
\[
\chi^2_0 = \text{(Round to three decimal places as needed)}
\]
3. **Choose the Correct Rejection Region Below:**
- A. \( \chi^2 < \chi^2_0 \)
- B. \( \chi^2 > \chi^2_0 \)
- C. \( \chi^2 < \chi^2_0 \)
- D. \( \chi^2 > \chi^2_0 \)
##### (c) Calculate the Test Statistics
- **Test Statistic (\( \chi^2 \)):**
\[
\chi^2 = \text{(Round to three decimal places as needed)}
\]
##### (d) Decision
Decide to reject or fail to reject the null hypothesis. Interpret the decision in the context of the original claim.
**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbd6a68d-f6ca-4106-a572-576a83876ff9%2F3116c6ca-3cc9-49f0-b3de-4477f87155c9%2Fam1ftsk_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Test: Relationship Between Skill Level and School Location
#### Problem Statement
Is achieving a basic skill level related to the location of the school? A random sample of students was surveyed, and their skill levels in three subjects (Reading, Math, Science) are shown in the contingency table below. At a significance level of α = 0.10, test the hypothesis that the variables are independent.
#### Contingency Table
| Location | Reading | Math | Science |
|-----------|---------|------|---------|
| Urban | 48 | 47 | 39 |
| Suburban | 62 | 60 | 69 |
#### Steps to Test Hypothesis
##### (a) Identify the Claim and State the Null and Alternative Hypotheses
- **Null Hypothesis (H₀):** Skill level in a subject is independent of location.
- **Alternative Hypothesis (H₁):** Skill level in a subject is dependent on location.
- **Claim:** (3) The claim is the alternative hypothesis.
##### (b) Determine the Degrees of Freedom, Find the Critical Value, and Identify the Rejection Region
1. **Degrees of Freedom (d.f.):**
\[
(\text{Number of rows} - 1) \times (\text{Number of columns} - 1) = (2 - 1) \times (3 - 1) = 2
\]
2. **Find the Critical Value:**
\[
\chi^2_0 = \text{(Round to three decimal places as needed)}
\]
3. **Choose the Correct Rejection Region Below:**
- A. \( \chi^2 < \chi^2_0 \)
- B. \( \chi^2 > \chi^2_0 \)
- C. \( \chi^2 < \chi^2_0 \)
- D. \( \chi^2 > \chi^2_0 \)
##### (c) Calculate the Test Statistics
- **Test Statistic (\( \chi^2 \)):**
\[
\chi^2 = \text{(Round to three decimal places as needed)}
\]
##### (d) Decision
Decide to reject or fail to reject the null hypothesis. Interpret the decision in the context of the original claim.
**
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman