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
icon
Related questions
Topic Video
Question
**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.
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman