### 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

Name: ### Constructing a 95% Confidence Interval for Population Mean#### Pr
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: ### 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

Answered: Image /qna-images/answer/b2adad9f-d727-4765-b0ac-6bdbdb636816.jpg

Math

Statistics

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

See similar textbooks

Similar questions

Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 90% 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? 249 210 177 164 164 163 152 152 152 147 What is the confidence interval estimate of the population mean µ? million < u< $ million (Round to one decimal place as needed.) What does the result tell us about the population of all celebrities? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. We are confident that 90% of all celebrities have a net worth between $ million and $ million. (Round to one decimal place as needed.) O B. We are 90% confident that the interval from $ million to $ million actually contains the true mean net worth of all celebrities. (Round to one decimal place as needed.) O C. Because the ten wealthiest celebrities…
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 normally distributed population as required? 244 214 182 164 161 157 150 150 150 150 What is the confidence interval estimate of the population mean u? $ million
Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 29 20 34 83 Female 43 26 25 94 Total 72 46 59 177 Use the table above to get a 90% confidence interval for the percentage of all female students who would receive a grade of A on this test.Enter your answers below using decimals. < P <
Listed below are the amounts of net worth in millions of the 10 wealthiest celebrities in a certain country. Construct a 90% confidence interval. What does the result tell us about the population of all the celebrities? Does the data appear to be from a normally distributed population as required? 247 208 196 173 166 161 148 148 143 143
Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel, May 19, 2018). Hotel occupancy data for February in two consecutive years are as follows, current year previous year occupied rooms 1470 1458 total rooms 1750 1800 a)What is the 95% confidence interval estimate of the change in occupancy for the one-year period? b)Do you think officials will be pleased with the results? c) Using a 0.05 level of significance, test the hypothesis that there has been an increase in the proportion of rooms occupied over the one-year period.
Thelma and Louise are each attempting to estimate the proportion of adults who enjoy listening to country music. They each survey a different random sample of adults, and in each sample, the proportion who say they enjoy listening to country music is 0.29. Thelma and Louise each use their sample data to construct a confidence interval. Thelma's interval is from 0.242 to 0.338 and Louise's interval is from 0.237 to 0.323. One of these intervals was computed correctly and the other was not. Which interval must be the correct one? It's impossible to answer this question without knowing the level of confidence used for each interval. It's impossible to answer this question without knowing the sample sizes. O It's impossible to answer this question without knowing the sample sizes or the level of confidence used for each interval. Thelma's interval must be the correct interval. O Louise's interval must be the correct interval.
Aaliyah wants to know if there is a difference between the proportions data in the following table. Construct a 95 % confidence interval for the true difference between the proportions of customers who just order water to drink at Restaurants A and B. Let Population 1 be the customers of Restaurant A and Population 2 be the customers of Restaurant B. Round the endpoints of the interval to customers who just order water to drink at two popular restaurants in town. She collected the three decimal places, if necessary. Drink orders Water Other Beverage Restaurant A 41 87 Restaurant B 87 62 Answer 囲 Tables 國 Keypad Keyboard Shortcuts Lower Endpoint = Upper Endpoint =
A survey of 32,782 adults in 2004 indicated that 24.6% of adults were current smokers. A similar study conducted in 1995 of 40,000 adults indicated that 29.7% were current smokers. a. Find and interpret a point estimate of the difference between the proportion of current smokers in 1995, and the proportion of current smokers in 2004. b. A 95% confidence interval for the true difference is (-0.058,-0.045). Interpret. c. What assumptions must you make for the confidence interval i part b to be valid? (…) a. Find a point estimate of the difference between the proportion of current smokers in 1995 and the proportion of current smokers in 2004. (Round to three decimal places as needed.)
Which of the following will increase the size of the confidence interval ?
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? 245 210 186 168 166 163 156 156 156 156
If the analyst decides to increase the sample size (n) from 75 to 100, while maintaining the same confidence level, the width of the confidence interval would then: fluctuate up and down. remain unchanged. decrease. increase.
QUESTION 28 A car insurance company wanted information about the age of its customers. A researcher computed 90%, 95%, 97%, and 99% confidence intervals for the population mean age of the customers. Which of the following intervals is the the 95% confidence interval for the population mean age? (36.30, 39.70) (36.70, 39.30) (36.56, 39.44) (36.91, 39.09)