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 38 business days, the mean closing price of a certain stock was $121.73. Assume the population standard deviation is $10.88. .... The 90% confidence interval is ( U ). (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. The 90% confidence interval 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 34 of the 38 days, and was within the 95% confidence interval for approximately 36 of the 38 days. O B. 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 C. 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 Next
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 38 business days, the mean closing price of a certain stock was $121.73. Assume the population standard deviation is $10.88. .... The 90% confidence interval is ( U ). (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. The 90% confidence interval 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 34 of the 38 days, and was within the 95% confidence interval for approximately 36 of the 38 days. O B. 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 C. 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 Next
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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![**Sample Mean and Confidence Intervals for Stock Prices**
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.
**Data provided:**
- From a random sample of 38 business days, the mean closing price of a certain stock was $121.73.
- Assume the population standard deviation is $10.88.
**Tasks:**
1. Calculate the 90% confidence interval.
- (Round to two decimal places as needed.)
2. Calculate the 95% confidence interval.
- (Round to two decimal places as needed.)
3. Determine which interval is wider. Choose the correct answer below:
- [ ] The 90% confidence interval
- [ ] The 95% confidence interval
**Interpret the results:**
A. You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 34 of the 38 days, and was within the 95% confidence interval for approximately 36 of the 38 days.
B. 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.
C. 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.
**Note:** Confidence intervals provide a range of values that are likely to contain the population mean, based on the sample data. A 95% confidence interval is generally wider than a 90% confidence interval, reflecting greater certainty.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a560b6e-7efb-42a9-961d-4ddfe6ff112f%2Fcf5fcbab-7876-4eac-b851-3ac9e1e04254%2Fznre0t5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Sample Mean and Confidence Intervals for Stock Prices**
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.
**Data provided:**
- From a random sample of 38 business days, the mean closing price of a certain stock was $121.73.
- Assume the population standard deviation is $10.88.
**Tasks:**
1. Calculate the 90% confidence interval.
- (Round to two decimal places as needed.)
2. Calculate the 95% confidence interval.
- (Round to two decimal places as needed.)
3. Determine which interval is wider. Choose the correct answer below:
- [ ] The 90% confidence interval
- [ ] The 95% confidence interval
**Interpret the results:**
A. You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 34 of the 38 days, and was within the 95% confidence interval for approximately 36 of the 38 days.
B. 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.
C. 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.
**Note:** Confidence intervals provide a range of values that are likely to contain the population mean, based on the sample data. A 95% confidence interval is generally wider than a 90% confidence interval, reflecting greater certainty.
![### Understanding Confidence Intervals in Stock Price Analysis
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 38 business days, the mean closing price of a certain stock was $121.73. Assume the population standard deviation is $10.88.
The 95% confidence interval is [_____, _____].
(Round to two decimal places as needed.)
**Which interval is wider? Choose the correct answer below:**
- ○ The 90% confidence interval
- ○ The 95% confidence interval
**Interpret the results.**
- **A.** You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 34 of the 38 days, and was within the 95% confidence interval for approximately 36 of the 38 days.
- **B.** 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.
- **C.** 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.
- **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.
Choose the option that best interprets the data, considering the definition of confidence intervals.
**Note:**
A confidence interval provides a range of values which is likely to contain the population mean. A wider interval suggests more uncertainty about the estimate of the population mean, while a narrower interval indicates more precision.
For educational purposes, select "Next" to proceed with understanding calculations and interpretations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a560b6e-7efb-42a9-961d-4ddfe6ff112f%2Fcf5fcbab-7876-4eac-b851-3ac9e1e04254%2Fdyhcx3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Confidence Intervals in Stock Price Analysis
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 38 business days, the mean closing price of a certain stock was $121.73. Assume the population standard deviation is $10.88.
The 95% confidence interval is [_____, _____].
(Round to two decimal places as needed.)
**Which interval is wider? Choose the correct answer below:**
- ○ The 90% confidence interval
- ○ The 95% confidence interval
**Interpret the results.**
- **A.** You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 34 of the 38 days, and was within the 95% confidence interval for approximately 36 of the 38 days.
- **B.** 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.
- **C.** 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.
- **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.
Choose the option that best interprets the data, considering the definition of confidence intervals.
**Note:**
A confidence interval provides a range of values which is likely to contain the population mean. A wider interval suggests more uncertainty about the estimate of the population mean, while a narrower interval indicates more precision.
For educational purposes, select "Next" to proceed with understanding calculations and interpretations.
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