In a survey of 905 U.S. adults who follow baseball in a recent year, 192 said that the Boston Red Sox would win the World Series. Construct a 95% confidence interval for the population proportion of U.S. adults who follow baseball who in a recent year said that the Boston Red Sox would win the World Series. (Round all calculations off to 3 decimal places.) p-hat q-hat = 1 - phat Confidence Level z value where p-hat = x/n (round off to 3 decimal places) %3D %3D Margin of Error where M. of E. = z*SQRT(phat*qhat)/n) Point Estimate Lower Limit Upper Limit Interpret the confidence interval in context of the problem

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question

I need help finding the answers that go into the yellow boxes :) Thank you so much! 

### Constructing a 95% Confidence Interval for Population Proportion

**Example Context: Boston Red Sox World Series Prediction**

In a survey of 905 U.S. adults who follow baseball in a recent year, 192 said that the Boston Red Sox would win the World Series. Construct a 95% confidence interval for the population proportion of U.S. adults who follow baseball who in a recent year said that the Boston Red Sox would win the World Series. 

**Note:** Round all calculations off to 3 decimal places.

---

#### Table with Detailed Calculations

| Item | Value | Formula/Explanation |
|------|-------|---------------------|
| **n**  | 905   | Total number of survey respondents |
| **x**  | 192   | Number of respondents who said Red Sox would win |
| **p-hat** | 0.212 | \(\hat{p} = \frac{x}{n}\) (round off to 3 decimal places) |
| **q-hat** | 0.788 | \(\hat{q} = 1 - \hat{p}\) |
| **Confidence Level** | 95% | Given in the problem |
| **z value** | 1.96 | Z value for 95% confidence level |
| **Margin of Error** | | \(\text{M. of E.} = z \times \sqrt{\frac{\hat{p} \times \hat{q}}{n}}\) |

#### Final Calculations

1. **Point Estimate:** \(\hat{p} = \frac{192}{905} = 0.212\)
2. **Margin of Error Calculation:**

    - \(\hat{q} = 1 - \hat{p} = 1 - 0.212 = 0.788\)
    - \( \text{Standard Error (SE)} = \sqrt{\frac{\hat{p} \times \hat{q}}{n}} = \sqrt{\frac{0.212 \times 0.788}{905}} \approx 0.014 \)
    - \(\text{Margin of Error (M. of E.)} = z \times \text{SE} = 1.96 \times 0.014 \approx 0.027\)

3. **Confidence Interval Limits:**
    - **Lower Limit:** \
Transcribed Image Text:### Constructing a 95% Confidence Interval for Population Proportion **Example Context: Boston Red Sox World Series Prediction** In a survey of 905 U.S. adults who follow baseball in a recent year, 192 said that the Boston Red Sox would win the World Series. Construct a 95% confidence interval for the population proportion of U.S. adults who follow baseball who in a recent year said that the Boston Red Sox would win the World Series. **Note:** Round all calculations off to 3 decimal places. --- #### Table with Detailed Calculations | Item | Value | Formula/Explanation | |------|-------|---------------------| | **n** | 905 | Total number of survey respondents | | **x** | 192 | Number of respondents who said Red Sox would win | | **p-hat** | 0.212 | \(\hat{p} = \frac{x}{n}\) (round off to 3 decimal places) | | **q-hat** | 0.788 | \(\hat{q} = 1 - \hat{p}\) | | **Confidence Level** | 95% | Given in the problem | | **z value** | 1.96 | Z value for 95% confidence level | | **Margin of Error** | | \(\text{M. of E.} = z \times \sqrt{\frac{\hat{p} \times \hat{q}}{n}}\) | #### Final Calculations 1. **Point Estimate:** \(\hat{p} = \frac{192}{905} = 0.212\) 2. **Margin of Error Calculation:** - \(\hat{q} = 1 - \hat{p} = 1 - 0.212 = 0.788\) - \( \text{Standard Error (SE)} = \sqrt{\frac{\hat{p} \times \hat{q}}{n}} = \sqrt{\frac{0.212 \times 0.788}{905}} \approx 0.014 \) - \(\text{Margin of Error (M. of E.)} = z \times \text{SE} = 1.96 \times 0.014 \approx 0.027\) 3. **Confidence Interval Limits:** - **Lower Limit:** \
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Fundamentals of Algebraic Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman