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A poll of 1055 Americans showed that 47% of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.05 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution. Ho: P H₁: p < (Type integers or decimals. Do not round.) Identify the test statistic. 2=0 (Round to two decimal places as needed.). Identify the P-value. IKEERD P-value= (Round to three decimal places as needed.) State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. the null hypothesis. There sufficient evidence to listen to it. Ythe claim that fewer than half of Americans prefer to watch the news rather than read or

A poll of 1055 Americans showed that 47% of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.05 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution. Ho: P H₁: p < (Type integers or decimals. Do not round.) Identify the test statistic. 2=0 (Round to two decimal places as needed.). Identify the P-value. IKEERD P-value= (Round to three decimal places as needed.) State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. the null hypothesis. There sufficient evidence to listen to it. Ythe claim that fewer than half of Americans prefer to watch the news rather than read or

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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The text contains details about a statistical hypothesis test conducted on a poll of 1055 Americans. It reports that 47% of the respondents prefer to watch the news rather than read or listen to it. The test uses a 0.05 significance level to evaluate the claim that fewer than half of Americans prefer watching the news over reading or listening to it. The methodology involves the P-value method, with normal distribution used as an approximation to the binomial distribution. The text includes spaces for filling in the null and alternative hypotheses, test statistic, P-value, and final conclusions. #### Fields to Fill: - **H0 (Null Hypothesis):** Example: \( p = 0.5 \), indicates that 50% of Americans prefer to watch the news. - **H1 (Alternative Hypothesis):** Example: \( p < 0.5 \), indicates that fewer than 50% prefer to watch the news. - **Test Statistic (z):** Space to insert the calculated value, rounded to two decimal places. - **P-value:** Space to insert the P-value, rounded to three decimal places. - **Conclusion:** Space to state whether the null hypothesis is rejected or not and the implication on the original claim. The interface seems to be designed to enter statistical values and draw conclusions based on hypothesis testing in a research context, ensuring a comprehensive understanding of a population's media consumption preferences.
Transcribed Image Text:The text contains details about a statistical hypothesis test conducted on a poll of 1055 Americans. It reports that 47% of the respondents prefer to watch the news rather than read or listen to it. The test uses a 0.05 significance level to evaluate the claim that fewer than half of Americans prefer watching the news over reading or listening to it. The methodology involves the P-value method, with normal distribution used as an approximation to the binomial distribution. The text includes spaces for filling in the null and alternative hypotheses, test statistic, P-value, and final conclusions. #### Fields to Fill: - **H0 (Null Hypothesis):** Example: \( p = 0.5 \), indicates that 50% of Americans prefer to watch the news. - **H1 (Alternative Hypothesis):** Example: \( p < 0.5 \), indicates that fewer than 50% prefer to watch the news. - **Test Statistic (z):** Space to insert the calculated value, rounded to two decimal places. - **P-value:** Space to insert the P-value, rounded to three decimal places. - **Conclusion:** Space to state whether the null hypothesis is rejected or not and the implication on the original claim. The interface seems to be designed to enter statistical values and draw conclusions based on hypothesis testing in a research context, ensuring a comprehensive understanding of a population's media consumption preferences.
Certainly! Below is a transcription of the text as it would appear on an educational website, along with an explanation of the relevant concepts, including hypotheses and statistical testing: --- **Statistical Analysis of News Consumption Preferences** A poll of 1055 Americans showed that 47% of the respondents prefer to watch the news rather than read or listen to it. Use these results with a 0.05 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. The normal distribution is used as an approximation to the binomial distribution. **Hypothesis Testing** Let \( p \) denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it. Identify the null and alternative hypotheses. - **Null Hypothesis (\( H_0 \))**: \( p = 0.5 \) - **Alternative Hypothesis (\( H_1 \))**: \( p < 0.5 \) **Identify the Test Statistic** The test statistic in a hypothesis test is calculated as follows: \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \] Where: - \( \hat{p} \) is the sample proportion (in this case, 0.47). - \( p_0 \) is the hypothesized population proportion (0.5). - \( n \) is the sample size (1055). (Round to two decimal places as needed.) **Identify the P-value** The P-value is determined by comparing the test statistic \( z \) to the standard normal distribution. (Round to three decimal places as needed.) **Conclusion** State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. --- **Explanation of Graphs or Diagrams** If any graphs or diagrams were present, they would be explained here, including specific details about axes, curves, and any data points shown. Typically, a diagram might include a normal distribution curve to highlight the critical region for the test statistic and the location of the calculated P-value. --- This text lays the groundwork for understanding the statistical test being performed, with a focus on hypothesis testing, and how it relates to the claim being analyzed.
Transcribed Image Text:Certainly! Below is a transcription of the text as it would appear on an educational website, along with an explanation of the relevant concepts, including hypotheses and statistical testing: --- **Statistical Analysis of News Consumption Preferences** A poll of 1055 Americans showed that 47% of the respondents prefer to watch the news rather than read or listen to it. Use these results with a 0.05 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. The normal distribution is used as an approximation to the binomial distribution. **Hypothesis Testing** Let \( p \) denote the population proportion of all Americans who prefer to watch the news rather than read or listen to it. Identify the null and alternative hypotheses. - **Null Hypothesis (\( H_0 \))**: \( p = 0.5 \) - **Alternative Hypothesis (\( H_1 \))**: \( p < 0.5 \) **Identify the Test Statistic** The test statistic in a hypothesis test is calculated as follows: \[ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \] Where: - \( \hat{p} \) is the sample proportion (in this case, 0.47). - \( p_0 \) is the hypothesized population proportion (0.5). - \( n \) is the sample size (1055). (Round to two decimal places as needed.) **Identify the P-value** The P-value is determined by comparing the test statistic \( z \) to the standard normal distribution. (Round to three decimal places as needed.) **Conclusion** State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. --- **Explanation of Graphs or Diagrams** If any graphs or diagrams were present, they would be explained here, including specific details about axes, curves, and any data points shown. Typically, a diagram might include a normal distribution curve to highlight the critical region for the test statistic and the location of the calculated P-value. --- This text lays the groundwork for understanding the statistical test being performed, with a focus on hypothesis testing, and how it relates to the claim being analyzed.
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