One study, based on responses from 1,011 randomly selected teenagers, concluded that 41% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of pressure. Formulate the null and alternative hypotheses. Choose the correct answer below. O A. Ho: p=0.5 OB. Ho: p=0.5 Ha: p<0.5 Ha: p > 0.5 O C. Ho: p=0.5 Ha: p *0.5 O D. Ho: p<0.5 Ha: p=0.5 Find the test statistic. z= (Round to two decimal places as needed.) Find the P-value for the found test statistic. P-value = (Round to four decimal places as needed.) State the conclusion. Choose the correct answer below. O A. Reject Ho. There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure. B. Do not reject Ho. There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
One study, based on responses from 1,011 randomly selected teenagers, concluded that 41% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of pressure. Formulate the null and alternative hypotheses. Choose the correct answer below. O A. Ho: p=0.5 OB. Ho: p=0.5 Ha: p<0.5 Ha: p > 0.5 O C. Ho: p=0.5 Ha: p *0.5 O D. Ho: p<0.5 Ha: p=0.5 Find the test statistic. z= (Round to two decimal places as needed.) Find the P-value for the found test statistic. P-value = (Round to four decimal places as needed.) State the conclusion. Choose the correct answer below. O A. Reject Ho. There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure. B. Do not reject Ho. There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
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
Question
![### Hypothesis Testing for Proportion
A study, based on responses from 1,011 randomly selected teenagers, concluded that 41% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of pressure.
---
**Formulate the Null and Alternative Hypotheses. Choose the correct answer below:**
- **A.** \( H_0: p = 0.5 \)
\( H_a: p > 0.5 \)
- **B.** \( H_0: p = 0.5 \)
\( H_a: p < 0.5 \)
- **C.** \( H_0: p = 0.5 \)
\( H_a: p \neq 0.5 \)
- **D.** \( H_0: p < 0.5 \)
\( H_a: p = 0.5 \)
**Find the Test Statistic:**
\[ z = \boxed{\text{(Round to two decimal places as needed.)}} \]
**Find the P-value for the found test statistic:**
\[ \text{P-value} = \boxed{\text{(Round to four decimal places as needed.)}} \]
**State the Conclusion. Choose the correct answer below:**
- **A.** Reject \( H_0 \). There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
- **B.** Do not reject \( H_0 \). There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
---
#### Instructions for Finding the Test Statistic and P-Value:
1. **Compute the Test Statistic:**
Use the formula for the Z-test for proportions:
\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \]
Where:
- \(\hat{p}\) is the sample proportion (0.41)
- \( p_0 \) is the population proportion in the null hypothesis (0.50)
- \( n \) is the sample size](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a448b68-b882-4133-a49b-44585a3f695e%2F5466ba6d-06a1-4a52-9cdb-a6178ba19279%2Fyme920u_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Proportion
A study, based on responses from 1,011 randomly selected teenagers, concluded that 41% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of pressure.
---
**Formulate the Null and Alternative Hypotheses. Choose the correct answer below:**
- **A.** \( H_0: p = 0.5 \)
\( H_a: p > 0.5 \)
- **B.** \( H_0: p = 0.5 \)
\( H_a: p < 0.5 \)
- **C.** \( H_0: p = 0.5 \)
\( H_a: p \neq 0.5 \)
- **D.** \( H_0: p < 0.5 \)
\( H_a: p = 0.5 \)
**Find the Test Statistic:**
\[ z = \boxed{\text{(Round to two decimal places as needed.)}} \]
**Find the P-value for the found test statistic:**
\[ \text{P-value} = \boxed{\text{(Round to four decimal places as needed.)}} \]
**State the Conclusion. Choose the correct answer below:**
- **A.** Reject \( H_0 \). There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
- **B.** Do not reject \( H_0 \). There is sufficient evidence to support the claim that fewer than half of all teenagers in the population feel that grades are the greatest source of pressure.
---
#### Instructions for Finding the Test Statistic and P-Value:
1. **Compute the Test Statistic:**
Use the formula for the Z-test for proportions:
\[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} \]
Where:
- \(\hat{p}\) is the sample proportion (0.41)
- \( p_0 \) is the population proportion in the null hypothesis (0.50)
- \( n \) is the sample size
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
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