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
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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.
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
Step 1: Introducing the given information

Sample size (n) = 800

p0 = 0.56

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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.
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.
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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.
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.
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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.

---
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. ---
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