A random sample of the closing stock prices in dollars for a company in recent year is listed below. Assume that o is $2.05. Construct the 90% a 99% confidence intervals for the population mean. Interpret the results a compare the widths of the confidence intervals. 20.05 17.49 21.71 22.72 16.95 16.51 20.45 17.97 17.81 16.34 18.73 15.67 15.41 19.13 16.84 15.54 The 90% confidence interval is ($ 17.24,$18.92). (Round to two decimal places as needed.) The 99% confidence interval is ($.$. ound to two do od)
A random sample of the closing stock prices in dollars for a company in recent year is listed below. Assume that o is $2.05. Construct the 90% a 99% confidence intervals for the population mean. Interpret the results a compare the widths of the confidence intervals. 20.05 17.49 21.71 22.72 16.95 16.51 20.45 17.97 17.81 16.34 18.73 15.67 15.41 19.13 16.84 15.54 The 90% confidence interval is ($ 17.24,$18.92). (Round to two decimal places as needed.) The 99% confidence interval is ($.$. ound to two do od)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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![### Confidence Intervals for Stock Prices
A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that the population standard deviation (σ) is $2.05. Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.
#### Stock Prices Sample:
- 20.05, 17.49, 21.71, 22.72, 17.81
- 16.34, 18.73, 15.67, 17.97, 16.95
- 16.51, 20.45, 15.54, 15.41, 19.13
- 16.84
---
#### Calculated Confidence Intervals:
- **90% Confidence Interval:** ($17.24, $18.92)
- *Rounded to two decimal places as needed.*
- **99% Confidence Interval:** ($__, $__)
- *Round to two decimal places as needed.*
---
### Explanation
The confidence intervals represent the range within which we expect the true population mean of the stock prices to fall. The 90% confidence interval is narrower than the 99% confidence interval, reflecting less certainty about the range but more precision. As the confidence level increases, the interval widens, incorporating more potential values of the population mean.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38aa5034-1eec-4964-a430-19a44c4ef4d5%2F383a9017-a8d0-42c8-9674-c35be84db6b9%2Ftcwp0ff_processed.png&w=3840&q=75)
Transcribed Image Text:### Confidence Intervals for Stock Prices
A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that the population standard deviation (σ) is $2.05. Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.
#### Stock Prices Sample:
- 20.05, 17.49, 21.71, 22.72, 17.81
- 16.34, 18.73, 15.67, 17.97, 16.95
- 16.51, 20.45, 15.54, 15.41, 19.13
- 16.84
---
#### Calculated Confidence Intervals:
- **90% Confidence Interval:** ($17.24, $18.92)
- *Rounded to two decimal places as needed.*
- **99% Confidence Interval:** ($__, $__)
- *Round to two decimal places as needed.*
---
### Explanation
The confidence intervals represent the range within which we expect the true population mean of the stock prices to fall. The 90% confidence interval is narrower than the 99% confidence interval, reflecting less certainty about the range but more precision. As the confidence level increases, the interval widens, incorporating more potential values of the population mean.
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