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Twenty years ago, 48% 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 234 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= 0.01 level of significance. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). 10, the sample size is Because npo (1-po) = 800 the requirements for testing the hypothesis (Round to one decimal place as needed.) satisfied. I 5% of the population size, and the sample

Twenty years ago, 48% 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 234 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= 0.01 level of significance. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). 10, the sample size is Because npo (1-po) = 800 the requirements for testing the hypothesis (Round to one decimal place as needed.) satisfied. I 5% of the population size, and the sample

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 11PPS
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### Statistical Problem: Parent Opinions on High School Education --- #### Background: Twenty years ago, 48% 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 out of 800 parents of children in high school, 234 believed it was a serious problem that high school students were not being taught enough math and science. We aim to determine if parents' opinions have changed over the past twenty years, using a 0.01 level of significance. --- #### Hypothesis Testing: **Null Hypothesis (H0):** \( p = 0.48 \) **Alternative Hypothesis (H1):** \( p \neq 0.48 \) #### Required Calculations: 1. **Sample Proportion (\( \hat{p} \)):** \[ \hat{p} = \frac{234}{800} = 0.2925 \] 2. **Determining Sample Adequacy:** Because \( np_0 (1 - p_0) = 800 \times 0.48 \times (1 - 0.48) = 192 \), we need to check that this value is greater than 10. --- #### Inputs Needed: - Sample Size (\( n \)): This would generally be calculated within a given framework, but the representation should indicate the sample size utilized, which is 800 in this case. - Proportion of Population (p_0): The population proportion twenty years ago was 0.48. --- **Interactive Graph Requirements:** An interactive interface is presented for the students to input values for \( np_0 (1 - p_0) = 800 \times 0.48 \times 0.52 \), illustrating that the sample size and conditions satisfy the requirements for hypothesis testing. #### Visual Aids: Considering the statistical nature of the problem, students may be provided links to the "Standard Normal Distribution Table" for reference. These can aid in understanding the Z-scores and critical values required to reach a conclusion. #### Educational Insights: - Students should be encouraged to understand the significance of verifying \( np_0 (1 - p_0) \geq 10 \) and how it convinces us that the sample distribution approximates normality. - Emphasis should be on the steps for testing hypotheses
Transcribed Image Text:### Statistical Problem: Parent Opinions on High School Education --- #### Background: Twenty years ago, 48% 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 out of 800 parents of children in high school, 234 believed it was a serious problem that high school students were not being taught enough math and science. We aim to determine if parents' opinions have changed over the past twenty years, using a 0.01 level of significance. --- #### Hypothesis Testing: **Null Hypothesis (H0):** \( p = 0.48 \) **Alternative Hypothesis (H1):** \( p \neq 0.48 \) #### Required Calculations: 1. **Sample Proportion (\( \hat{p} \)):** \[ \hat{p} = \frac{234}{800} = 0.2925 \] 2. **Determining Sample Adequacy:** Because \( np_0 (1 - p_0) = 800 \times 0.48 \times (1 - 0.48) = 192 \), we need to check that this value is greater than 10. --- #### Inputs Needed: - Sample Size (\( n \)): This would generally be calculated within a given framework, but the representation should indicate the sample size utilized, which is 800 in this case. - Proportion of Population (p_0): The population proportion twenty years ago was 0.48. --- **Interactive Graph Requirements:** An interactive interface is presented for the students to input values for \( np_0 (1 - p_0) = 800 \times 0.48 \times 0.52 \), illustrating that the sample size and conditions satisfy the requirements for hypothesis testing. #### Visual Aids: Considering the statistical nature of the problem, students may be provided links to the "Standard Normal Distribution Table" for reference. These can aid in understanding the Z-scores and critical values required to reach a conclusion. #### Educational Insights: - Students should be encouraged to understand the significance of verifying \( np_0 (1 - p_0) \geq 10 \) and how it convinces us that the sample distribution approximates normality. - Emphasis should be on the steps for testing hypotheses
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