### Constructing a 95% Confidence Interval for Population Mean#### Problem StatementListed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 95% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required?**Net Worth Data (in millions of dollars):**- 257- 215- 198- 175- 159- 153- 153- 153- 150- 148#### TaskWhat is the confidence interval estimate of the population mean $ \mu $?\[ \boxed{} \text{ million} < \mu < \boxed{} \text{ million} \](Round to one decimal place as needed.)### ExplanationTo construct a 95% confidence interval for the population mean, follow these steps:1. **Calculate the Sample Mean ($ \bar{x} $)**: Add all the net worth values, and then divide by the number of observations (10 in this case). \[ \bar{x} = \frac{\sum x_i}{n} = \frac{257 + 215 + 198 + 175 + 159 + 153 + 153 + 153 + 150 + 148}{10} \]2. **Calculate the Sample Standard Deviation (s)**: Use the formula for the standard deviation of a sample. \[ s = \sqrt{ \frac{\sum (x_i - \bar{x})^2}{n-1} } \]3. **Determine the t-Score for a 95% Confidence Interval**: Look up the t-value for $ n-1 $ degrees of freedom (in this case, 9 degrees of freedom) and a 95% confidence level in a t-distribution table.4. **Construct the Confidence Interval**: Use the formula: \[ \text{CI} = \bar{x} \pm t \times \frac{s}{\sqrt{n}} \]5. **Interpret the Results**: This interval gives a range of values within which we can be 95% confident that the population mean $ \mu $ lies. The result also helps to understand if the data

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Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 95% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required? 257 215 198 175 159 153 153 153 150 148 What is the confidence interval estimate of the population mean u? $ million < u<$ million (Round to one decimal place as needed.)

Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 95% confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required? 257 215 198 175 159 153 153 153 150 148 What is the confidence interval estimate of the population mean u? $ million < u<$ million (Round to one decimal place as needed.)

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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