In December 2004, 43% of students in high school were satisfied with the lunches supplied through the school. In May 2010, an organization conducted a poll of 1046 students in high school and asked if they were satisfied with the lunches supplied through the school. Of the 1046 surveyed, 397 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 x = 0.10 level of significance, compute the probability of making a Type II error, ß, if the true population proportion is 0.38. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.42. (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 0.43. O B. Ho is rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.43. OC. Ho is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is equal to 0.43. (b) If the researcher decides to test this hypothesis at the α = 0.10 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.38. 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 0.42. B = Power = (Type integers or decimals rounded to four decimal places as needed.) ☐☐
In December 2004, 43% of students in high school were satisfied with the lunches supplied through the school. In May 2010, an organization conducted a poll of 1046 students in high school and asked if they were satisfied with the lunches supplied through the school. Of the 1046 surveyed, 397 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 x = 0.10 level of significance, compute the probability of making a Type II error, ß, if the true population proportion is 0.38. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.42. (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 0.43. O B. Ho is rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.43. OC. Ho is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is equal to 0.43. (b) If the researcher decides to test this hypothesis at the α = 0.10 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.38. 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 0.42. 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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Question
![### Decrease in Satisfaction with School Lunches Over Time: A Hypothesis Test
In December 2004, 43% of high school students were satisfied with the lunches supplied through the school. In May 2010, an organization conducted a poll of 1046 students in high school and asked if they were satisfied with the lunches supplied through the school. Of the 1046 surveyed, 397 indicated they were satisfied. Does this suggest the proportion of students satisfied with the quality of lunches has decreased?
This example tests a hypothesis about whether the satisfaction with school lunches has decreased from 43% (2004) to a lower proportion based on the 2010 survey.
#### (a) Understanding Type II Error
**Question:**
What does it mean to make a Type II error for this test?
**Options:**
- **A.** H₀ is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.43.
- **B.** H₀ is rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.43.
- **C.** H₀ is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is equal to 0.43.
#### (b) Computation of Power of the Test
**Question:**
If the researcher decides to test this hypothesis at the α = 0.10 level of significance, compute the probability of making a Type II error (β), if the true population proportion is 0.38. What is the power of the test?
- β = [Calculation Required]
- Power = [Calculation Required]
*(Type integers or decimals rounded to four decimal places as needed.)*
#### (c) Power of the Test with Different True Proportion
**Question:**
Redo part (b) if the true population proportion is 0.42.
- β = [Calculation Required]
- Power = [Calculation Required]
*(Type integers or decimals rounded to four decimal places as needed.)*
### Explanation of Concepts
- **Type II Error (β):** Occurs when the null hypothesis (H₀) is not rejected when it is actually false.
- **Power of a Test:** Probability that the test correctly rejects a false null hypothesis, calculated as \( 1 - β \).
This problem illustrates the application of hypothesis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e2dce9f-bcdf-4f32-a081-371e2dab1fcb%2F0a08c212-8b49-40ec-83b5-de4d39ed519a%2Fr5pz2d_processed.png&w=3840&q=75)
Transcribed Image Text:### Decrease in Satisfaction with School Lunches Over Time: A Hypothesis Test
In December 2004, 43% of high school students were satisfied with the lunches supplied through the school. In May 2010, an organization conducted a poll of 1046 students in high school and asked if they were satisfied with the lunches supplied through the school. Of the 1046 surveyed, 397 indicated they were satisfied. Does this suggest the proportion of students satisfied with the quality of lunches has decreased?
This example tests a hypothesis about whether the satisfaction with school lunches has decreased from 43% (2004) to a lower proportion based on the 2010 survey.
#### (a) Understanding Type II Error
**Question:**
What does it mean to make a Type II error for this test?
**Options:**
- **A.** H₀ is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.43.
- **B.** H₀ is rejected and the true proportion of high school students who are not satisfied with the quality of lunches is less than 0.43.
- **C.** H₀ is not rejected and the true proportion of high school students who are not satisfied with the quality of lunches is equal to 0.43.
#### (b) Computation of Power of the Test
**Question:**
If the researcher decides to test this hypothesis at the α = 0.10 level of significance, compute the probability of making a Type II error (β), if the true population proportion is 0.38. What is the power of the test?
- β = [Calculation Required]
- Power = [Calculation Required]
*(Type integers or decimals rounded to four decimal places as needed.)*
#### (c) Power of the Test with Different True Proportion
**Question:**
Redo part (b) if the true population proportion is 0.42.
- β = [Calculation Required]
- Power = [Calculation Required]
*(Type integers or decimals rounded to four decimal places as needed.)*
### Explanation of Concepts
- **Type II Error (β):** Occurs when the null hypothesis (H₀) is not rejected when it is actually false.
- **Power of a Test:** Probability that the test correctly rejects a false null hypothesis, calculated as \( 1 - β \).
This problem illustrates the application of hypothesis
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