A random sample of 18 venture-capital investments in a certain business sector yielded the accompanying data, in millions of dollars. Assuming that the population standard deviation is $1.78 million, a 95% confidence interval for the mean amount, µ, of all venture-capital investments in this business sector is from $5.65 million to $7.30 million. Conditions for computing the confidence interval are satisfied. Complete parts (a) through (d) below. (Note: The sum of the data is $116.52 million and the mean is $6.47 million.) Click here to view the investment data. Click here to view page 1 of the table of areas under the standard normal curve, Click here to view page 2 of the table of areas under the standard normal curve, a. Find a 90% confidence interval for u. The 90% confidence interval is from $ million to $ million. Investment data (Round to two decimal places as needed.) 5.93 6.83 6.46 9.67 3.17 5.39 5.98 5.64 3.85 8.73 6.44 7.16 4.25 8.09 8.81 5.20 8.27 6.65
A random sample of 18 venture-capital investments in a certain business sector yielded the accompanying data, in millions of dollars. Assuming that the population standard deviation is $1.78 million, a 95% confidence interval for the mean amount, µ, of all venture-capital investments in this business sector is from $5.65 million to $7.30 million. Conditions for computing the confidence interval are satisfied. Complete parts (a) through (d) below. (Note: The sum of the data is $116.52 million and the mean is $6.47 million.) Click here to view the investment data. Click here to view page 1 of the table of areas under the standard normal curve, Click here to view page 2 of the table of areas under the standard normal curve, a. Find a 90% confidence interval for u. The 90% confidence interval is from $ million to $ million. Investment data (Round to two decimal places as needed.) 5.93 6.83 6.46 9.67 3.17 5.39 5.98 5.64 3.85 8.73 6.44 7.16 4.25 8.09 8.81 5.20 8.27 6.65
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Solve from A to D
- [Table of areas under the standard normal curve - Page 2](#)
This exercise helps in understanding the application of statistical methods to real-world financial data, essential for making informed investment decisions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2b425c8-1e3a-4bc4-9526-e999f44a089d%2F54793152-30f8-488a-a135-88cfc9b6c6c1%2F7x4mjms_processed.png&w=3840&q=75)
Transcribed Image Text:# Confidence Interval Calculation for Venture-Capital Investments
A random sample of 18 venture-capital investments in a certain business sector yielded data in millions of dollars. Assuming that the population standard deviation is $1.78 million, a 95% confidence interval for the mean amount, µ, of all venture-capital investments in this sector is from $5.65 million to $7.30 million. Conditions for computing the confidence interval are satisfied.
### Investment Data
The data is presented in a matrix with three rows and six columns:
- Row 1: 5.93, 6.83, 6.46, 9.67, 3.17, 5.39
- Row 2: 5.98, 5.64, 3.85, 8.73, 6.44, 7.16
- Row 3: 4.25, 8.09, 8.81, 5.20, 8.27, 6.65
Total sum of the data is $116.52 million, and the mean is $6.47 million.
### Task
a. Find a 90% confidence interval for µ.
The 90% confidence interval is from $ ___ million to $ ___ million.
(Round to two decimal places as needed.)
### Additional Resources
- [Table of areas under the standard normal curve - Page 1](#)
- [Table of areas under the standard normal curve - Page 2](#)
This exercise helps in understanding the application of statistical methods to real-world financial data, essential for making informed investment decisions.
![**Transcription: Educational Website Content**
**b. Why is the confidence interval you found in part (a) shorter than the 95% confidence interval?**
The [Value] used in computing the confidence interval found in part (a) is [less than] the corresponding value for the 95% confidence interval.
**c. Draw a graph to display both confidence intervals. Choose the correct graph below.**
- **Option A:** Displays a 95% CI for µ above a wider interval with a 90% CI for µ below a narrower interval on a number line ranging from 4 to 7, with 5.5 marked as the central point.
- **Option B:** Displays a 95% CI for µ as a wider interval and a 90% CI for µ as a narrower interval directly below it on a number line ranging from 4 to 7, with 5.5 as the central point. (Selected Option)
- **Option C:** Displays a 90% CI for µ above and a 95% CI for µ below with inversion compared to Option A on a number line ranging from 4 to 7.
- **Option D:** Displays a 90% CI for µ as a wider interval and a 95% CI for µ as a narrower interval below it on a number line ranging from 4 to 7.
**d. Which confidence interval yields a more accurate estimate of µ? Explain your answer.**
[The 95% CI] yields a more accurate estimate of µ, since [it provides a higher level of confidence].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2b425c8-1e3a-4bc4-9526-e999f44a089d%2F54793152-30f8-488a-a135-88cfc9b6c6c1%2Fcuno2c_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription: Educational Website Content**
**b. Why is the confidence interval you found in part (a) shorter than the 95% confidence interval?**
The [Value] used in computing the confidence interval found in part (a) is [less than] the corresponding value for the 95% confidence interval.
**c. Draw a graph to display both confidence intervals. Choose the correct graph below.**
- **Option A:** Displays a 95% CI for µ above a wider interval with a 90% CI for µ below a narrower interval on a number line ranging from 4 to 7, with 5.5 marked as the central point.
- **Option B:** Displays a 95% CI for µ as a wider interval and a 90% CI for µ as a narrower interval directly below it on a number line ranging from 4 to 7, with 5.5 as the central point. (Selected Option)
- **Option C:** Displays a 90% CI for µ above and a 95% CI for µ below with inversion compared to Option A on a number line ranging from 4 to 7.
- **Option D:** Displays a 90% CI for µ as a wider interval and a 95% CI for µ as a narrower interval below it on a number line ranging from 4 to 7.
**d. Which confidence interval yields a more accurate estimate of µ? Explain your answer.**
[The 95% CI] yields a more accurate estimate of µ, since [it provides a higher level of confidence].
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