**Confidence Interval and Population Proportion Analysis**A 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. 71 of the 727 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible.**Questions:**a. With 95% 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 727 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.**Hint:**- **Hints**: [ ] - **Video**: [+] **Explanation:**Understanding confidence intervals and population proportions is essential in statistical analysis. A confidence interval provides a range of values which is likely to contain the population parameter with a certain degree of confidence. When constructing a 95% confidence interval, it means that if we were to take numerous samples and construct a confidence interval from each sample, approximately 95% of these intervals will contain the true population proportion, while 5% will not.**Steps to Calculate a Confidence Interval for Proportion:**1. **Calculate the sample proportion (p̂):** \[ p̂ = \frac{\text{number of successes}}{\text{sample size}} \] Here, number of successes = 71 and sample size = 727. 2. **Calculate the standard error (SE) of the sample proportion:** \[ SE = \sqrt{\frac{p̂ (1 - p̂)}{n}} \] Where \( p̂ \) is the sample proportion and \( n \) is the sample size. 3. **Find the critical value (z*) for a 95% confidence level:** The critical value for a 95% confidence level is 1.96. 4. **Construct the confidence interval:** \[ p̂ \pm (z

a. The provided information is x=71 n=727 The sample proportion is p^=xn=71727=0.097The level of…

Answered: A psychologist is interested in…

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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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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