Homework Help is Here – Start Your Trial Now!
Math
Statistics
A survey was conducted that asked 1017 people how many books they had read in the past year. Results indicated that x = 12.2 books and s= 16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval. Click the icon to view the table of critical t-values. H Construct a 90% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice (Use ascending order. Round to two decimal places as needed.) OA. If repeated samples are taken, 90% of them will have a sample mean between and OB. There is 90% confidence that the population mean number of books read is between and OC. There is a 90% probability that the true mean number of books read is between and

A survey was conducted that asked 1017 people how many books they had read in the past year. Results indicated that x = 12.2 books and s= 16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval. Click the icon to view the table of critical t-values. H Construct a 90% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice (Use ascending order. Round to two decimal places as needed.) OA. If repeated samples are taken, 90% of them will have a sample mean between and OB. There is 90% confidence that the population mean number of books read is between and OC. There is a 90% probability that the true mean number of books read is between and

MATLAB: An Introduction with Applications
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
icon
Related questions
Question
**Constructing a 90% Confidence Interval for Mean Number of Books Read** A survey was conducted that asked 1017 people how many books they had read in the past year. Results indicated that the sample mean (\( \bar{x} \)) is 12.2 books and the sample standard deviation (s) is 16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval. **Step-by-Step Guide:** 1. **Identify the sample mean (\( \bar{x} \)) and the sample standard deviation (s)):** - Sample mean (\( \bar{x} \)): 12.2 books - Sample standard deviation (s): 16.6 books 2. **Calculate the standard error of the mean (SE):** - Formula: \( SE = \frac{s}{\sqrt{n}} \) - Where: - \( s \) = sample standard deviation - \( n \) = sample size - Calculation: \( SE = \frac{16.6}{\sqrt{1017}} \) 3. **Determine the critical value (z*) for a 90% confidence interval:** - For a 90% confidence interval, the critical value (\( z^* \)) is approximately 1.645. This value can be obtained from the standard normal (Z) distribution table. 4. **Calculate the margin of error (ME):** - Formula: \( ME = z^* \times SE \) - Calculation: \( ME = 1.645 \times SE \) 5. **Compute the confidence interval:** - Formula: \( \left( \bar{x} - ME, \bar{x} + ME \right) \) - Calculation: \( \left( 12.2 - ME, 12.2 + ME \right) \) 6. **Interpret the confidence interval:** - Construct a 90% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice using ascending order. Round to two decimal places as needed. **Choices:** - **A.** If repeated samples are taken, 90% of them will have a sample mean between \(\_\_\) and \(\_\_\). - **B
Transcribed Image Text:**Constructing a 90% Confidence Interval for Mean Number of Books Read** A survey was conducted that asked 1017 people how many books they had read in the past year. Results indicated that the sample mean (\( \bar{x} \)) is 12.2 books and the sample standard deviation (s) is 16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval. **Step-by-Step Guide:** 1. **Identify the sample mean (\( \bar{x} \)) and the sample standard deviation (s)):** - Sample mean (\( \bar{x} \)): 12.2 books - Sample standard deviation (s): 16.6 books 2. **Calculate the standard error of the mean (SE):** - Formula: \( SE = \frac{s}{\sqrt{n}} \) - Where: - \( s \) = sample standard deviation - \( n \) = sample size - Calculation: \( SE = \frac{16.6}{\sqrt{1017}} \) 3. **Determine the critical value (z*) for a 90% confidence interval:** - For a 90% confidence interval, the critical value (\( z^* \)) is approximately 1.645. This value can be obtained from the standard normal (Z) distribution table. 4. **Calculate the margin of error (ME):** - Formula: \( ME = z^* \times SE \) - Calculation: \( ME = 1.645 \times SE \) 5. **Compute the confidence interval:** - Formula: \( \left( \bar{x} - ME, \bar{x} + ME \right) \) - Calculation: \( \left( 12.2 - ME, 12.2 + ME \right) \) 6. **Interpret the confidence interval:** - Construct a 90% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice using ascending order. Round to two decimal places as needed. **Choices:** - **A.** If repeated samples are taken, 90% of them will have a sample mean between \(\_\_\) and \(\_\_\). - **B
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
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
SEE MORE TEXTBOOKS