### Confidence Interval Analysis in Psychological ResearchA psychologist is interested in constructing a 95% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. In a survey, 64 out of 739 randomly selected people agreed with this theory. The answers should be rounded to 4 decimal places where possible.#### Questions:**a.** With 95% confidence, what is the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain?The 95% confidence interval is between \_\_\_\_\_ and \_\_\_\_\_.**b.** If many groups of 739 randomly selected people are surveyed, different confidence intervals would be produced from each group. What percentage of these confidence intervals will contain the true population proportion of all people who accept the theory?\_\_\_\_\_ percent of these confidence intervals will contain the true population proportion, and about \_\_\_\_\_ percent will not contain the true population proportion.#### Explanation for Graphs or Diagrams:There are no graphs or diagrams included in this text. However, if there were any, they would visually display the range of the confidence intervals, with the 95% confidence interval typically shown as a shaded region between two values on a number line. This visualization helps to illustrate the range within which we can be 95% confident that the true population proportion lies, based on our sample data.### Calculation GuidanceTo determine the 95% confidence interval for this scenario, the usual formula used is:\[ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]Where:- \( \hat{p} \) is the sample proportion (64/739).- \( Z \) is the Z-score corresponding to the 95% confidence level (approximately 1.96).- \( n \) is the sample size (739).For the percentages asked in part (b), recall that:- For a 95% confidence interval, 95% of the intervals will contain the true population proportion.- Thus, 5% of the intervals will not contain the true population proportion.

Sample size n = 739x=64confidence level=95%Sample proportion()= = 0.0866

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A psychologist is interested in constructing a 90% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 68 of the 807 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between___and___ . b. If many groups of 807 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About__ percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about____ percent will not contain the true population proportion.
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Chapter 11 2. Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation. A random sample of 200 students was selected from a large college in the United States. Each selected student was asked to give his or her opinion about the following statement. "The most important quality of a person who aspires to be the President of the United States is a knowledge of foreign affairs." Each response was recorded in one of five categories. The gender of each selected student was noted. The data are summarized in the table below. Page 2 of 4 Response Category Strongly Somewhat Disagree Male 10 Disagree 15 Neither Agree nor Disagree Somewhat Strongly Agree Agree 15 25 25 Female 20 25 25 25 15 Is there sufficient evidence to indicate that the response is dependent on gender? Provide statistical evidence to support your conclusion. AP Statistics
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