Here are summary statistics for randomly selected weights of newborn girls: n=198, x =32.7 hg, s = 7.8 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 30.4 hg
Here are summary statistics for randomly selected weights of newborn girls: n=198, x =32.7 hg, s = 7.8 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 30.4 hg
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 a Confidence Interval for Newborn Girls' Weights**
Below are the summary statistics for randomly selected weights of newborn girls:
- Sample Size (n): 198
- Sample Mean (\(\bar{x}\)): 32.7 hg
- Sample Standard Deviation (s): 7.8 hg
We will construct a confidence interval estimate of the mean using a 98% confidence level. Additionally, we will compare these results to the confidence interval 30.4 hg < \(\mu\) < 34.6 hg, which was constructed using a smaller sample size of 19 with the following summary statistics:
- Sample Mean (\(\bar{x}\)): 32.5 hg
- Sample Standard Deviation (s): 3.6 hg
**Question:**
What is the confidence interval for the population mean \(\mu\)?
Enter the values in the provided fields:
\[ \boxed{\ \ } \text{ hg } < \mu < \boxed{\ \ } \text{ hg } \]
(Round to one decimal place as needed.)
To determine the confidence interval, we will need to calculate the margin of error using the appropriate statistical methods, taking into account the sample size and the standard deviation. The steps typically involve identifying the critical value for the specified confidence level and using the formula for the confidence interval:
\[ \text{Confidence Interval} = \left( \bar{x} - \text{Margin of Error}, \bar{x} + \text{Margin of Error} \right) \]
This interval will give us a range in which we can be 98% confident that the true population mean lies.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77118ecc-eadc-491f-9762-2009f6b89d99%2F91807993-b222-4b7e-bcb4-a063614ebd86%2Fy74kmd.jpeg&w=3840&q=75)
Transcribed Image Text:**Constructing a Confidence Interval for Newborn Girls' Weights**
Below are the summary statistics for randomly selected weights of newborn girls:
- Sample Size (n): 198
- Sample Mean (\(\bar{x}\)): 32.7 hg
- Sample Standard Deviation (s): 7.8 hg
We will construct a confidence interval estimate of the mean using a 98% confidence level. Additionally, we will compare these results to the confidence interval 30.4 hg < \(\mu\) < 34.6 hg, which was constructed using a smaller sample size of 19 with the following summary statistics:
- Sample Mean (\(\bar{x}\)): 32.5 hg
- Sample Standard Deviation (s): 3.6 hg
**Question:**
What is the confidence interval for the population mean \(\mu\)?
Enter the values in the provided fields:
\[ \boxed{\ \ } \text{ hg } < \mu < \boxed{\ \ } \text{ hg } \]
(Round to one decimal place as needed.)
To determine the confidence interval, we will need to calculate the margin of error using the appropriate statistical methods, taking into account the sample size and the standard deviation. The steps typically involve identifying the critical value for the specified confidence level and using the formula for the confidence interval:
\[ \text{Confidence Interval} = \left( \bar{x} - \text{Margin of Error}, \bar{x} + \text{Margin of Error} \right) \]
This interval will give us a range in which we can be 98% confident that the true population mean lies.
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