You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 44 business days, the mean closing price of a certain stock was $122.38. Assume the population standard deviation is $10.29. The 90% confidence interval is. (Round to two decimal places as needed.) The 95% confidence interval is (.). (Round to two decimal places as needed.) Which interval is wider? Choose the correct answer below. O The 90% confidence interval O The 95% confidence interval Interpret the results. ・・・ O A. You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 40 of the 44 days, and was within the 95% confidence interval for approximately 42 of the 44 days. O B. You can be 90% confident that the population mean price of the stock is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval. O C. You can be 90% confident that the population mean price of the stock is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval. O D. You can be certain that the population mean price of the stock is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals.
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of 44 business days, the mean closing price of a certain stock was $122.38. Assume the population standard deviation is $10.29. The 90% confidence interval is. (Round to two decimal places as needed.) The 95% confidence interval is (.). (Round to two decimal places as needed.) Which interval is wider? Choose the correct answer below. O The 90% confidence interval O The 95% confidence interval Interpret the results. ・・・ O A. You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 40 of the 44 days, and was within the 95% confidence interval for approximately 42 of the 44 days. O B. You can be 90% confident that the population mean price of the stock is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval. O C. You can be 90% confident that the population mean price of the stock is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval. O D. You can be certain that the population mean price of the stock is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals.
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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![### Constructing Confidence Intervals for Population Mean
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.
**Scenario:**
From a random sample of 44 business days, the mean closing price of a certain stock was $122.38. Assume the population standard deviation is $10.29.
---
**Confidence Intervals Calculation:**
1. **90% Confidence Interval:**
\[
( \Box, \Box )
\]
(Round to two decimal places as needed.)
2. **95% Confidence Interval:**
\[
( \Box, \Box )
\]
(Round to two decimal places as needed.)
**Question:**
Which interval is wider? Choose the correct answer below.
- ○ The 90% confidence interval
- ○ The 95% confidence interval
**Interpretation of Results:**
a. You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 40 of the 44 days, and was within the 95% confidence interval for approximately 42 of the 44 days.
b. You can be 90% confident that the population mean price of the stock is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval.
c. You can be 90% confident that the population mean price of the stock is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.
d. You can be certain that the population mean price of the stock is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals.
---
### Explanation of Concepts:
**Confidence Interval:**
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. The interval has an associated confidence level that quantifies the level of confidence that the parameter lies within the range.
**Comparison of Interval Widths:**
The width of a confidence interval depends on the confidence level chosen. Typically, a higher confidence level (e.g., 95%) will result in a wider interval, while a lower confidence level (e.g., 90%) will result in a narrower interval. The trade](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe21ad11-6e18-4b63-a679-8109648f0f0b%2F66193d16-b8c8-4b31-a8f2-808346ed385a%2F81a3ej_processed.png&w=3840&q=75)
Transcribed Image Text:### Constructing Confidence Intervals for Population Mean
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.
**Scenario:**
From a random sample of 44 business days, the mean closing price of a certain stock was $122.38. Assume the population standard deviation is $10.29.
---
**Confidence Intervals Calculation:**
1. **90% Confidence Interval:**
\[
( \Box, \Box )
\]
(Round to two decimal places as needed.)
2. **95% Confidence Interval:**
\[
( \Box, \Box )
\]
(Round to two decimal places as needed.)
**Question:**
Which interval is wider? Choose the correct answer below.
- ○ The 90% confidence interval
- ○ The 95% confidence interval
**Interpretation of Results:**
a. You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 40 of the 44 days, and was within the 95% confidence interval for approximately 42 of the 44 days.
b. You can be 90% confident that the population mean price of the stock is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval.
c. You can be 90% confident that the population mean price of the stock is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.
d. You can be certain that the population mean price of the stock is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals.
---
### Explanation of Concepts:
**Confidence Interval:**
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. The interval has an associated confidence level that quantifies the level of confidence that the parameter lies within the range.
**Comparison of Interval Widths:**
The width of a confidence interval depends on the confidence level chosen. Typically, a higher confidence level (e.g., 95%) will result in a wider interval, while a lower confidence level (e.g., 90%) will result in a narrower interval. The trade
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