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In 1996, 57% of high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. A recent survey found that 110 of 200 high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. Do high school teachers feel differently today than they did in 1996? (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 α = 0.10 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.55. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.52.

In 1996, 57% of high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. A recent survey found that 110 of 200 high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. Do high school teachers feel differently today than they did in 1996? (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 α = 0.10 level of significance, compute the probability of making a Type II error, B, if the true population proportion is 0.55. What is the power of the test? (c) Redo part (b) if the true population proportion is 0.52.

MATLAB: An Introduction with Applications
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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Only need answers to b and c. Thanks!
### Teacher Perceptions of Student Attentiveness Over Time In 1996, 57% of high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. A recent survey found that 110 of 200 high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. Do high school teachers feel differently today than they did in 1996? #### Questions: **(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 \( \alpha = 0.10 \) level of significance, compute the probability of making a Type II error, \( \beta \), if the true population proportion is 0.55. What is the power of the test? **(c)** Redo part (b) if the true population proportion is 0.52. ### Explanations: **Type II Error Explanation**: - A **Type II error (β)** occurs when the test fails to reject a false null hypothesis. In this context, it means not detecting a change in the proportion of teachers who believe student attentiveness is a serious problem when there actually is a change. **Steps for Calculating Type II Error (β) and Power**: 1. **Determine the null and alternative hypotheses**. - Null hypothesis (\( H_0 \)): The proportion of teachers who think it's a serious problem is still 57% (\( p = 0.57 \)). - Alternative hypothesis (\( H_a \)): The proportion of teachers who think it's a serious problem is different from 57% (\( p \neq 0.57 \)). 2. **Identify the sample proportion**: - Sample proportion ( \( \hat{p} \) ) = \( \frac{110}{200} = 0.55 \). 3. **Calculate z-scores for the critical values under \( H_0 \)**. 4. **Compute the probability of Type II error (β) for given true proportions**. 5. **Calculate the power of the test** as \( 1 - β \). ### Example Computations for (b) and (c): Let's denote z as the critical value. **For part (b)**: - True population proportion = 0.55 - Determine the critical z-values for \(
Transcribed Image Text:### Teacher Perceptions of Student Attentiveness Over Time In 1996, 57% of high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. A recent survey found that 110 of 200 high school teachers felt it was a serious problem that high school students were not being attentive enough in the classroom. Do high school teachers feel differently today than they did in 1996? #### Questions: **(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 \( \alpha = 0.10 \) level of significance, compute the probability of making a Type II error, \( \beta \), if the true population proportion is 0.55. What is the power of the test? **(c)** Redo part (b) if the true population proportion is 0.52. ### Explanations: **Type II Error Explanation**: - A **Type II error (β)** occurs when the test fails to reject a false null hypothesis. In this context, it means not detecting a change in the proportion of teachers who believe student attentiveness is a serious problem when there actually is a change. **Steps for Calculating Type II Error (β) and Power**: 1. **Determine the null and alternative hypotheses**. - Null hypothesis (\( H_0 \)): The proportion of teachers who think it's a serious problem is still 57% (\( p = 0.57 \)). - Alternative hypothesis (\( H_a \)): The proportion of teachers who think it's a serious problem is different from 57% (\( p \neq 0.57 \)). 2. **Identify the sample proportion**: - Sample proportion ( \( \hat{p} \) ) = \( \frac{110}{200} = 0.55 \). 3. **Calculate z-scores for the critical values under \( H_0 \)**. 4. **Compute the probability of Type II error (β) for given true proportions**. 5. **Calculate the power of the test** as \( 1 - β \). ### Example Computations for (b) and (c): Let's denote z as the critical value. **For part (b)**: - True population proportion = 0.55 - Determine the critical z-values for \(
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