Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 308 of 800 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the a= 0.05 level of significance. Because npo (1-Po) = 10, the sample size is (Round to one decimal place as needed.) 5% of the population size, and the sample ▼the requirements for testing the hypothesis satisfied.
Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 308 of 800 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the a= 0.05 level of significance. Because npo (1-Po) = 10, the sample size is (Round to one decimal place as needed.) 5% of the population size, and the sample ▼the requirements for testing the hypothesis satisfied.
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
![Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 308 of 800 parents of children in high
school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the α = 0.05 level of significance.
Because npo (1-Po)
10, the sample size is
(Round to one decimal place as needed.)
=
5% of the population size, and the sample
the requirements for testing the hypothesis
satisfied.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac3be618-b645-4bd8-855b-808ff3fc18d4%2F787f00cf-d825-4e9a-8c31-c5e13a3b0a4b%2Fqmjeler_processed.png&w=3840&q=75)
Transcribed Image Text:Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 308 of 800 parents of children in high
school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the α = 0.05 level of significance.
Because npo (1-Po)
10, the sample size is
(Round to one decimal place as needed.)
=
5% of the population size, and the sample
the requirements for testing the hypothesis
satisfied.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1: Introducing the given information
Sample size (n) = 800
p0 = 0.56
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
![### Statistical Analysis of Parental Opinions on Math and Science Education
**Background**
Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. In a recent survey, 308 out of 800 parents felt similarly. This analysis seeks to determine if parental opinions have shifted over twenty years, using a significance level of α = 0.05.
**Sampling and Assumptions**
- The product of the sample size (n) and the initial proportion (p₀) is calculated as:
\[ n₀p₀(1 - p₀) = 197.1 \]
- This value is greater than 10.
- The sample size is less than 5% of the population size and can be reasonably assumed to be random, thus satisfying the conditions for hypothesis testing.
**Hypotheses**
- **Null Hypothesis (H₀):** \( p = 0.56 \)
- **Alternative Hypothesis (H₁):** \( p \neq 0.56 \)
**Test Statistic**
- Calculated z-value:
\[ z₀ = -9.97 \]
(Rounded to two decimal places as needed)
**P-Value Calculation**
- P-value:
\[ \text{P-value} = \, \]
(Round to three decimal places as needed)
This analysis aids in understanding whether there is a significant change in parental opinion regarding the adequacy of math and science education in high schools over the past two decades.](https://content.bartleby.com/qna-images/question/ac3be618-b645-4bd8-855b-808ff3fc18d4/ecfde4e7-a37a-4ea4-adc0-9a68d785deb4/80w9bka_thumbnail.png)
Transcribed Image Text:### Statistical Analysis of Parental Opinions on Math and Science Education
**Background**
Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. In a recent survey, 308 out of 800 parents felt similarly. This analysis seeks to determine if parental opinions have shifted over twenty years, using a significance level of α = 0.05.
**Sampling and Assumptions**
- The product of the sample size (n) and the initial proportion (p₀) is calculated as:
\[ n₀p₀(1 - p₀) = 197.1 \]
- This value is greater than 10.
- The sample size is less than 5% of the population size and can be reasonably assumed to be random, thus satisfying the conditions for hypothesis testing.
**Hypotheses**
- **Null Hypothesis (H₀):** \( p = 0.56 \)
- **Alternative Hypothesis (H₁):** \( p \neq 0.56 \)
**Test Statistic**
- Calculated z-value:
\[ z₀ = -9.97 \]
(Rounded to two decimal places as needed)
**P-Value Calculation**
- P-value:
\[ \text{P-value} = \, \]
(Round to three decimal places as needed)
This analysis aids in understanding whether there is a significant change in parental opinion regarding the adequacy of math and science education in high schools over the past two decades.
Solution
Follow-up Question
![Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 308 of 800 parents of children in high
school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the α = 0.05 level of significance.
Because npo (1-Po) = 197.1 > 10, the sample size is
(Round to one decimal place as needed.)
What are the null and alternative hypotheses?
0.56 versus H₁: p # 0.56
Ho: P
(Type integers or decimals. Do not round.)
Find the test statistic.
Zo (Round to two decimal places as needed.)
less than 5% of the population size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied.](https://content.bartleby.com/qna-images/question/ac3be618-b645-4bd8-855b-808ff3fc18d4/8c74296e-1174-435d-8118-688243e44bc9/swrwi4m_thumbnail.png)
Transcribed Image Text:Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 308 of 800 parents of children in high
school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the α = 0.05 level of significance.
Because npo (1-Po) = 197.1 > 10, the sample size is
(Round to one decimal place as needed.)
What are the null and alternative hypotheses?
0.56 versus H₁: p # 0.56
Ho: P
(Type integers or decimals. Do not round.)
Find the test statistic.
Zo (Round to two decimal places as needed.)
less than 5% of the population size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied.
Solution
Follow-up Question
![**Transcription and Explanation for Educational Website**
---
**Context:**
Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 308 of 800 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the \( \alpha = 0.05 \) level of significance.
---
**Analysis Steps:**
1. **Sample Size Verification:**
- Calculation: \( n p_0 (1 - p_0) = 197.1 \)
- Comparison: This value is greater than 10, indicating the sample size is sufficiently large.
2. **Sample Proportion Context:**
- The sample size is **less than** 5% of the population size.
- The sample **can be reasonably assumed to be random**.
3. **Conclusion for Testing Requirements:**
- The requirements for testing the hypothesis **are** satisfied.
---
**Hypotheses:**
- Null Hypothesis (\( H_0 \)): [Dropdown or input necessary]
- Alternative Hypothesis (\( H_1 \)): [Dropdown or input necessary]
*(Type integers or decimals. Do not round.)*
---
### Diagram/Graph Explanation:
There is no explicit diagram or graph included in the content provided, only a structured logical framework for hypothesis testing.
### Notes for Educators:
- Ensure students understand how to calculate the test statistic and determine whether the sample conditions meet the requirements for hypothesis testing.
- Encourage critical analysis of the assumptions behind using a random sample and its implications on the results of the hypothesis test.
---](https://content.bartleby.com/qna-images/question/ac3be618-b645-4bd8-855b-808ff3fc18d4/fe5646ff-e6e4-428e-b972-61af3ae2dbba/arg7agl_thumbnail.png)
Transcribed Image Text:**Transcription and Explanation for Educational Website**
---
**Context:**
Twenty years ago, 56% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 308 of 800 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the \( \alpha = 0.05 \) level of significance.
---
**Analysis Steps:**
1. **Sample Size Verification:**
- Calculation: \( n p_0 (1 - p_0) = 197.1 \)
- Comparison: This value is greater than 10, indicating the sample size is sufficiently large.
2. **Sample Proportion Context:**
- The sample size is **less than** 5% of the population size.
- The sample **can be reasonably assumed to be random**.
3. **Conclusion for Testing Requirements:**
- The requirements for testing the hypothesis **are** satisfied.
---
**Hypotheses:**
- Null Hypothesis (\( H_0 \)): [Dropdown or input necessary]
- Alternative Hypothesis (\( H_1 \)): [Dropdown or input necessary]
*(Type integers or decimals. Do not round.)*
---
### Diagram/Graph Explanation:
There is no explicit diagram or graph included in the content provided, only a structured logical framework for hypothesis testing.
### Notes for Educators:
- Ensure students understand how to calculate the test statistic and determine whether the sample conditions meet the requirements for hypothesis testing.
- Encourage critical analysis of the assumptions behind using a random sample and its implications on the results of the hypothesis test.
---
Solution
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