A survey was conducted that asked 1009 people how many books they had read in the past year. Results indicated that X= 14.4 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. 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 OB. There is a 90% probability that the true mean number of books read is between OC. There is 90% confidence that the population mean number of books read is between and D and and
A survey was conducted that asked 1009 people how many books they had read in the past year. Results indicated that X= 14.4 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. 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 OB. There is a 90% probability that the true mean number of books read is between OC. There is 90% confidence that the population mean number of books read is between and D and and
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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Transcribed Image Text:### Educational Content on Constructing a Confidence Interval
A survey was conducted that asked 1009 people how many books they had read in the past year. Results indicated that the sample mean (\( \bar{x} \)) was 14.4 books and the standard deviation (s) was 16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval.
**Steps to Construct a 90% Confidence Interval:**
1. **Identify the Parameters:**
- Sample Mean (\( \bar{x} \)): 14.4 books
- Standard Deviation (s): 16.6 books
- Sample Size (n): 1009
2. **Determine the Critical Value:**
- Use a t-table to find the critical t-value for a 90% confidence interval and a sample size of 1009 (typically use z-value for large n).
3. **Calculate the Margin of Error (ME):**
- ME = Critical Value \(\times\) (s/√n)
4. **Construct the Confidence Interval:**
- Lower Limit = \( \bar{x} \) - ME
- Upper Limit = \( \bar{x} \) + ME
5. **Interpret the Confidence Interval:**
- There is 90% confidence that the population mean number of books read is between the lower and upper limit.
**Multiple Choice Interpretation:**
Select the correct choice and fill in the answer boxes:
A. If repeated samples are taken, 90% of them will have a sample mean between __ and __.
B. There is a 90% probability that the true mean number of books read is between __ and __.
C. There is 90% confidence that the population mean number of books read is between __ and __.
**Note:** Choose option C for the correct interpretation of a confidence interval.
By following these steps and understanding the interpretation, you can effectively construct and understand confidence intervals in statistical research.
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