### 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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