Consider the following questions about CIs (Confidence intervals).  A researcher tests emotional intelligence (EI) for a random sample of children selected from a population of all students who are enrolled in a school for gifted children. The researcher wants to estimate the mean emotional intelligence EI for the entire school. The population standard deviation, , for EI is not known. Let’s suppose that a researcher wants to set up a 95% (Confidence intervals) CI for IQ scores using the following information: The sample mean M = 130. The sample standard deviation s = 15. The sample size N =120. The (degree of freedom) df = N – 1 = 119. pg 87 df = 120 – 1 = 119 df = 119 For the values given above, the limits of the 95% CI are as follows: Lower limit = 130 – 1.96 x 1.37 = 127.31; Upper limit = 130 + 1.96 x 1.37 = 132.69. The following exercises ask you to experiment to see how changing some of the values involved in computing the CI influences the width of the CI. Recalculate the CI above to see how the lower and upper limits (and the width of the CI) change as you vary the N in the sample (and leave all the other values the same). What are the upper and lower limits and the width of the CI if you change the confidence level to 80% (and continue to use M = 130, s = 15, and N = 49)? For the 80% CI, lower limit = ___________ and upper limit = ____________.   Width (upper limit - lower limit)= ____________________________. What are the upper and lower limits and the width of the CI if you change the confidence level to 99% (continue to use M = 130, s = 15 and N = 49)? For a 99% CI, lower limit = __________ and upper limit = _____________.  Width (upper limit - lower limit) = _____________________________. How does increasing the level of confidence from 80% to 99% affect the width of the CI?

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
Question

Consider the following questions about CIs (Confidence intervals). 

A researcher tests emotional intelligence (EI) for a random sample of children selected from a population of all students who are enrolled in a school for gifted children. The researcher wants to estimate the mean emotional intelligence EI for the entire school. The population standard deviation, , for EI is not known.

Let’s suppose that a researcher wants to set up a 95% (Confidence intervals) CI for IQ scores using the following information:

The sample mean M = 130.

The sample standard deviation s = 15.

The sample size N =120.

The (degree of freedom) df = N – 1 = 119. pg 87

df = 120 – 1 = 119

df = 119

For the values given above, the limits of the 95% CI are as follows:

Lower limit = 130 – 1.96 x 1.37 = 127.31;

Upper limit = 130 + 1.96 x 1.37 = 132.69.

The following exercises ask you to experiment to see how changing some of the values involved in computing the CI influences the width of the CI.

Recalculate the CI above to see how the lower and upper limits (and the width of the CI) change as you vary the N in the sample (and leave all the other values the same).

What are the upper and lower limits and the width of the CI if you change the confidence level to 80% (and continue to use M = 130, s = 15, and N = 49)?

For the 80% CI, lower limit = ___________ and upper limit = ____________.  

Width (upper limit - lower limit)= ____________________________.

What are the upper and lower limits and the width of the CI if you change the confidence level to 99% (continue to use M = 130, s = 15 and N = 49)?

For a 99% CI, lower limit = __________ and upper limit = _____________.

 Width (upper limit - lower limit) = _____________________________.

How does increasing the level of confidence from 80% to 99% affect the width of the CI?

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Anova and Design of Experiments
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