The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the a = 0.05 level of significance. Category 1 Category 2 Category 3 O Failures 54 57 45 Successes 77 36 66 State the hypotheses. Choose the correct answer below. O A. Ho: P1 =P2 = P3 H1: At least one of the proportions is different from the others. O B. Ho: The categories of the variable and success and failure are independent. H4: The categories of the variable and success and failure are dependent. O C. Ho: The categories of the variable and success and failure are dependent. H1: The categories of the variable and success and failure are independent. O D. Ho: H1 = E, and µ2 = E2 and µ3 = E3 H4: At least one mean is different from what is expected. What is the P-value? (Round to three decimal places as needed.) What conclusion can be made? O A. The P-value is less than a, so do not reject Ho. There is not sufficient evidence that the categories of the variable and success and failure are dependent. O B. The P-value is greater than or equal to a, so do not reject Ho. There is sufficient evidence that the categories of the variable and success and failure are dependent. OC. The P-value is less than a, so reject Ho: There is sufficient evidence that the proportions are different from each other. O D. The P-value is greater than or equal to a, so reject Ho. There is not sufficient evidence that the proportions are different from each other.
The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the a = 0.05 level of significance. Category 1 Category 2 Category 3 O Failures 54 57 45 Successes 77 36 66 State the hypotheses. Choose the correct answer below. O A. Ho: P1 =P2 = P3 H1: At least one of the proportions is different from the others. O B. Ho: The categories of the variable and success and failure are independent. H4: The categories of the variable and success and failure are dependent. O C. Ho: The categories of the variable and success and failure are dependent. H1: The categories of the variable and success and failure are independent. O D. Ho: H1 = E, and µ2 = E2 and µ3 = E3 H4: At least one mean is different from what is expected. What is the P-value? (Round to three decimal places as needed.) What conclusion can be made? O A. The P-value is less than a, so do not reject Ho. There is not sufficient evidence that the categories of the variable and success and failure are dependent. O B. The P-value is greater than or equal to a, so do not reject Ho. There is sufficient evidence that the categories of the variable and success and failure are dependent. OC. The P-value is less than a, so reject Ho: There is sufficient evidence that the proportions are different from each other. O D. The P-value is greater than or equal to a, so reject Ho. There is not sufficient evidence that the proportions are different from each other.
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
Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
![**Testing the Proportions in Different Categories**
The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the α = 0.05 level of significance.
| | Category 1 | Category 2 | Category 3 |
|--------------|:----------:|:----------:|:----------:|
| **Failures** | 54 | 57 | 45 |
| **Successes**| 77 | 36 | 66 |
**State the hypotheses. Choose the correct answer below:**
A. \( H_0: p_1 = p_2 = p_3 \)
\( H_1: \) At least one of the proportions is different from the others.
B. \( H_0: \) The categories of the variable and success and failure are independent.
\( H_1: \) The categories of the variable and success and failure are dependent.
C. \( H_0: \) The categories of the variable and success and failure are dependent.
\( H_1: \) The categories of the variable and success and failure are independent.
D. \( H_0: \mu_1 = E_1 \) and \( \mu_2 = E_2 \) and \( \mu_3 = E_3 \)
\( H_1: \) At least one mean is different from what is expected.
**What is the P-value?**
[ ] **(Round to three decimal places as needed)**
**What conclusion can be made?**
A. The P-value is less than α, so do not reject \( H_0 \). There is not sufficient evidence that the categories of the variable and success and failure are dependent.
B. The P-value is greater than or equal to α, so do not reject \( H_0 \). There is sufficient evidence that the categories of the variable and success and failure are dependent.
C. The P-value is less than α, so reject \( H_0 \). There is sufficient evidence that the proportions are different from each other.
D. The P-value is greater than or equal to α, so reject \( H_0 \). There is not sufficient evidence that the proportions are different from each other.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4175707-d254-4126-a791-753312836f35%2Fa3300da7-af8c-4236-9be2-c56e45b3bd89%2Fcuya3p2_processed.png&w=3840&q=75)
Transcribed Image Text:**Testing the Proportions in Different Categories**
The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the α = 0.05 level of significance.
| | Category 1 | Category 2 | Category 3 |
|--------------|:----------:|:----------:|:----------:|
| **Failures** | 54 | 57 | 45 |
| **Successes**| 77 | 36 | 66 |
**State the hypotheses. Choose the correct answer below:**
A. \( H_0: p_1 = p_2 = p_3 \)
\( H_1: \) At least one of the proportions is different from the others.
B. \( H_0: \) The categories of the variable and success and failure are independent.
\( H_1: \) The categories of the variable and success and failure are dependent.
C. \( H_0: \) The categories of the variable and success and failure are dependent.
\( H_1: \) The categories of the variable and success and failure are independent.
D. \( H_0: \mu_1 = E_1 \) and \( \mu_2 = E_2 \) and \( \mu_3 = E_3 \)
\( H_1: \) At least one mean is different from what is expected.
**What is the P-value?**
[ ] **(Round to three decimal places as needed)**
**What conclusion can be made?**
A. The P-value is less than α, so do not reject \( H_0 \). There is not sufficient evidence that the categories of the variable and success and failure are dependent.
B. The P-value is greater than or equal to α, so do not reject \( H_0 \). There is sufficient evidence that the categories of the variable and success and failure are dependent.
C. The P-value is less than α, so reject \( H_0 \). There is sufficient evidence that the proportions are different from each other.
D. The P-value is greater than or equal to α, so reject \( H_0 \). There is not sufficient evidence that the proportions are different from each other.
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 3 steps
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