In December 2004, 35% of students in high school were satisfied with the lunches supplied through the school. In May 2010, an organization conducted a poll of 1083 students in high school and asked if they were satisfied with the lunches supplied through the school. Of the 1083 surveyed, 336 indicated they were satisfied. Does this suggest the proportion of students satisfied with the quality of lunches has decreased? (a) What does it mean to make a Type II error for this test? (b) If the researcher decides to test this hypothesis at the a = 0.10 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.31. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.34. (a) What does it mean to make a Type II error for this test? Choose the correct answer below. O A. Ho is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.35. O B. Ho is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is equal to 0.35. O C. Ho is rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.35. (b) If the researcher decides to test this hypothesis at the x = 0.10 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.31. What is the power of the test? B = Power = (Type integers or decimals rounded to four decimal places as needed.) (c) Redo part (b) if the true population proportion is 0.34. B = Power = (Type integers or decimals rounded to four decimal places as needed.)
In December 2004, 35% of students in high school were satisfied with the lunches supplied through the school. In May 2010, an organization conducted a poll of 1083 students in high school and asked if they were satisfied with the lunches supplied through the school. Of the 1083 surveyed, 336 indicated they were satisfied. Does this suggest the proportion of students satisfied with the quality of lunches has decreased? (a) What does it mean to make a Type II error for this test? (b) If the researcher decides to test this hypothesis at the a = 0.10 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.31. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.34. (a) What does it mean to make a Type II error for this test? Choose the correct answer below. O A. Ho is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.35. O B. Ho is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is equal to 0.35. O C. Ho is rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.35. (b) If the researcher decides to test this hypothesis at the x = 0.10 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.31. What is the power of the test? B = Power = (Type integers or decimals rounded to four decimal places as needed.) (c) Redo part (b) if the true population proportion is 0.34. B = Power = (Type integers or decimals rounded to four decimal places as needed.)
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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![### Hypothesis Testing in Population Proportion
#### Scenario:
In December 2004, 35% of students in high school were satisfied with the lunches supplied through the school. In May 2010, an organization conducted a poll of 1083 students in high school and asked if they were satisfied with the lunches supplied through the school. Of the 1083 surveyed, 336 indicated they were satisfied. Does this suggest the proportion of students satisfied with the quality of lunches has decreased?
### Questions:
**(a)** What does it mean to make a Type II error for this test?
**Answer Choices:**
- **A.** \(H_0\) is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.35.
- **B.** \(H_0\) is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is equal to 0.35.
- **C.** \(H_0\) is rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.35.
**(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.10 \) level of significance, compute the probability of making a Type II error, \( \beta \), if the true population proportion is 0.31. What is the power of the test?
**(c)** Redo part (b) if the true population proportion is 0.34.
### Inputs for Computation:
Below are the form fields for the user to input relevant values to determine \( \beta \) and Power.
- **(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.10 \) level of significance, compute the probability of making a Type II error, \( \beta \), if the true population proportion is 0.31.
- \( \beta = \) [Input Field]
- Power = [Input Field]
- *(Type integers or decimals rounded to four decimal places as needed.)*
- **(c)** Redo part (b) if the true population proportion is 0.34.
- \( \beta = \) [Input Field]
- Power = [Input Field]
- *(Type integers or decimals rounded to four decimal places as needed](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94a522d8-ef89-4b5b-a14c-d37c6cf2440e%2F065c8975-0a2a-419b-b2ae-9d2f8366e407%2Fdl31b0l_processed.png&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing in Population Proportion
#### Scenario:
In December 2004, 35% of students in high school were satisfied with the lunches supplied through the school. In May 2010, an organization conducted a poll of 1083 students in high school and asked if they were satisfied with the lunches supplied through the school. Of the 1083 surveyed, 336 indicated they were satisfied. Does this suggest the proportion of students satisfied with the quality of lunches has decreased?
### Questions:
**(a)** What does it mean to make a Type II error for this test?
**Answer Choices:**
- **A.** \(H_0\) is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.35.
- **B.** \(H_0\) is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is equal to 0.35.
- **C.** \(H_0\) is rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.35.
**(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.10 \) level of significance, compute the probability of making a Type II error, \( \beta \), if the true population proportion is 0.31. What is the power of the test?
**(c)** Redo part (b) if the true population proportion is 0.34.
### Inputs for Computation:
Below are the form fields for the user to input relevant values to determine \( \beta \) and Power.
- **(b)** If the researcher decides to test this hypothesis at the \( \alpha = 0.10 \) level of significance, compute the probability of making a Type II error, \( \beta \), if the true population proportion is 0.31.
- \( \beta = \) [Input Field]
- Power = [Input Field]
- *(Type integers or decimals rounded to four decimal places as needed.)*
- **(c)** Redo part (b) if the true population proportion is 0.34.
- \( \beta = \) [Input Field]
- Power = [Input Field]
- *(Type integers or decimals rounded to four decimal places as needed
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