Om are there? The number of degrees of freedom is 4 Part: 5/9 Part 6 of 9 State the null and alternate hypotheses. Below, p represents the probability of earning an A. Ho PA=, PB=U, Pc= PD=. PF =D H,: Some of the probabilities are not equal to the values specified by H.
Om are there? The number of degrees of freedom is 4 Part: 5/9 Part 6 of 9 State the null and alternate hypotheses. Below, p represents the probability of earning an A. Ho PA=, PB=U, Pc= PD=. PF =D H,: Some of the probabilities are not equal to the values specified by H.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Part 6 please
![**Statistical Hypothesis Testing: Understanding Null and Alternative Hypotheses**
In the context of statistical analysis, the hypotheses are crucial in testing the validity of an assumed parameter. Below is an explanation of how to state the null and alternative hypotheses for a given scenario:
---
### Part 5 / 9
**Number of Degrees of Freedom**
- The number of degrees of freedom is represented as: **4**
### Part 6 / 9
**Hypotheses Illustration**
We are tasked with stating the null and alternative hypotheses. In this setup, \( p_A \) represents the probability of earning a grade A.
**Null Hypothesis (\( H_0 \))**
\[
H_0: p_A = \, \_\_ \, , \, p_B = \, \_\_ \, , \, p_C = \, \_\_ \, , \, p_D = \, \_\_ \, , \, p_F = \, \_\_
\]
**Description:** The null hypothesis (\( H_0 \)) suggests that each probability \( p_A, p_B, p_C, p_D, \) and \( p_F \) is equal to a specified value. These values represent the probabilities of earning grades A, B, C, D, and F, respectively.
**Alternative Hypothesis (\( H_1 \))**
\[
H_1: \text{Some of the probabilities are not equal to the values specified by } H_0.
\]
**Description:** The alternative hypothesis (\( H_1 \)) posits that at least one of the probabilities is different from the values assumed in the null hypothesis.
---
**Understanding Graphs or Diagrams:**
No graphs or diagrams are present in the provided section. The focus here is on understanding the hypothesis statements and their implications in hypothesis testing.
For learners, the ability to correctly state \( H_0 \) and \( H_1 \) is a foundational skill in statistical analysis, essential for clear conclusions based on data evidence.
**Tools for Learning:**
- **Interactive Features:** The interface allows users to skip parts, check answers, and save progress, facilitating a dynamic learning environment.
---
This educational resource is designed to guide students and professionals alike in mastering hypothesis formulation and testing methods, fostering a comprehensive understanding of statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F509e8bce-9e19-472b-b32e-290ce2fb93cc%2Ff0c93944-cf58-41db-a5e5-24ddd8104ad5%2F1fi27i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Statistical Hypothesis Testing: Understanding Null and Alternative Hypotheses**
In the context of statistical analysis, the hypotheses are crucial in testing the validity of an assumed parameter. Below is an explanation of how to state the null and alternative hypotheses for a given scenario:
---
### Part 5 / 9
**Number of Degrees of Freedom**
- The number of degrees of freedom is represented as: **4**
### Part 6 / 9
**Hypotheses Illustration**
We are tasked with stating the null and alternative hypotheses. In this setup, \( p_A \) represents the probability of earning a grade A.
**Null Hypothesis (\( H_0 \))**
\[
H_0: p_A = \, \_\_ \, , \, p_B = \, \_\_ \, , \, p_C = \, \_\_ \, , \, p_D = \, \_\_ \, , \, p_F = \, \_\_
\]
**Description:** The null hypothesis (\( H_0 \)) suggests that each probability \( p_A, p_B, p_C, p_D, \) and \( p_F \) is equal to a specified value. These values represent the probabilities of earning grades A, B, C, D, and F, respectively.
**Alternative Hypothesis (\( H_1 \))**
\[
H_1: \text{Some of the probabilities are not equal to the values specified by } H_0.
\]
**Description:** The alternative hypothesis (\( H_1 \)) posits that at least one of the probabilities is different from the values assumed in the null hypothesis.
---
**Understanding Graphs or Diagrams:**
No graphs or diagrams are present in the provided section. The focus here is on understanding the hypothesis statements and their implications in hypothesis testing.
For learners, the ability to correctly state \( H_0 \) and \( H_1 \) is a foundational skill in statistical analysis, essential for clear conclusions based on data evidence.
**Tools for Learning:**
- **Interactive Features:** The interface allows users to skip parts, check answers, and save progress, facilitating a dynamic learning environment.
---
This educational resource is designed to guide students and professionals alike in mastering hypothesis formulation and testing methods, fostering a comprehensive understanding of statistical analysis.
Transcribed Image Text:**Grade Distribution Analysis**
A statistics teacher claims the following average grade distribution for her students:
- 5% receive a grade of A
- 8% receive a grade of B
- 61% receive a grade of C
- 16% receive a grade of D
- 10% receive a grade of F
To test this claim, a random sample of 100 students' grades was recorded. The results are presented in the table below:
| Grade | A | B | C | D | F |
|----------|----|----|----|----|----|
| Observed | 4 | 15 | 54 | 19 | 8 |
**Part 1 of 9**
- **Question:** How many of the students in the sample got a B? How many got an F?
- The number of students who got a B is **15**.
- The number of students who got an F is **8**.
**Part 2 of 9**
- **Task:** Compute the expected frequencies.
*Note: The table for expected frequencies is requested to be completed in this part, but specific values for expected frequencies are not calculated here.*
This analysis serves as an exercise in understanding statistical claims and how to evaluate them using observed data. Students will learn how to compute expected frequencies based on a theoretical distribution and compare them with observed frequencies to assess the validity of the original claim.
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