a = 0.05, n = 83, x = 66.4, s² = 2.88 to Interpret the interval that you have constructed. O In repeated sampling, 95% of all intervals constructed in this manner will enclose the population mean. In repeated sampling, 5% of all intervals constructed in this manner will enclose the population mean. There is a 95% chance that an individual sample mean will fall within the interval. O There is a 5% chance that an individual sample mean will fall within the interval. 95% of all values will fall within the interval.
a = 0.05, n = 83, x = 66.4, s² = 2.88 to Interpret the interval that you have constructed. O In repeated sampling, 95% of all intervals constructed in this manner will enclose the population mean. In repeated sampling, 5% of all intervals constructed in this manner will enclose the population mean. There is a 95% chance that an individual sample mean will fall within the interval. O There is a 5% chance that an individual sample mean will fall within the interval. 95% of all values will fall within the interval.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 11MCQ
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Question
I need help with all parts of this quesiton 18
![**Confidence Interval for a Population Mean**
Calculate the necessary confidence interval for a population mean \( \mu \) using the following values. Ensure to round your answers to two decimal places.
- Significance level (\( \alpha \)): 0.05
- Sample size (\( n \)): 83
- Sample mean (\( \bar{x} \)): 66.4
- Sample variance (\( s^2 \)): 2.88
**Confidence Interval Range:**
\[ \_\_\_\_\_\_ \text{ to } \_\_\_\_\_\_ \]
**Interpret the Constructed Interval:**
Choose the correct interpretation from the options below:
- ○ In repeated sampling, 95% of all intervals constructed in this manner will enclose the population mean.
- ○ In repeated sampling, 5% of all intervals constructed in this manner will enclose the population mean.
- ○ There is a 95% chance that an individual sample mean will fall within the interval.
- ○ There is a 5% chance that an individual sample mean will fall within the interval.
- ○ 95% of all values will fall within the interval.
This exercise will help you understand and apply the concept of confidence intervals in statistics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbff43673-f06b-43ca-b409-46eb420ace6b%2Ff3306b04-27af-4cec-b229-6acdddd67794%2Fazi2v4q_processed.png&w=3840&q=75)
Transcribed Image Text:**Confidence Interval for a Population Mean**
Calculate the necessary confidence interval for a population mean \( \mu \) using the following values. Ensure to round your answers to two decimal places.
- Significance level (\( \alpha \)): 0.05
- Sample size (\( n \)): 83
- Sample mean (\( \bar{x} \)): 66.4
- Sample variance (\( s^2 \)): 2.88
**Confidence Interval Range:**
\[ \_\_\_\_\_\_ \text{ to } \_\_\_\_\_\_ \]
**Interpret the Constructed Interval:**
Choose the correct interpretation from the options below:
- ○ In repeated sampling, 95% of all intervals constructed in this manner will enclose the population mean.
- ○ In repeated sampling, 5% of all intervals constructed in this manner will enclose the population mean.
- ○ There is a 95% chance that an individual sample mean will fall within the interval.
- ○ There is a 5% chance that an individual sample mean will fall within the interval.
- ○ 95% of all values will fall within the interval.
This exercise will help you understand and apply the concept of confidence intervals in statistics.
Expert Solution
Step 1
It is given that
X̄ = 66.4, n = 83
s2 = 2.88 => s = 1.697
α = 0.05
Confidence interval = 1 - α
= 1 - 0.05 = 0.95
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