Show that in Example 4.4.7, page 153, the difference between the two candidates is statistically significant even at a confidence level of 99.7%.

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

Show that in Example 4.4.7, page 153, the difference between the two candidates is statistically significant even at a confidence level of 99.7%.

Now to the numbers! Let's begin with Candidate A. We have the following
numbers: sample size n =
1350, favorable voters k
648. Therefore p
648
0.48 or 48%, and o 2
1350 x 0.48 х (1 — 0.48) ~ 18.3565, so the
1350
18.3565
standard error is st.err. -
a 0.0136 or 1.36%.
1350
CHAPTER 4. STATISTICS
153
This tells us that the percentage of support for Candidate A the day of
the poll was between 48 – 2 × 1.36 and 48+2×1.36, that is between 45.28%
and 50.72%.
Similarly, for Candidate B we have n =
1350, favorable voters k
702.
702
Therefore p =
— 0.52 or 52%, and o ~ y/1350 x 0.52 х (1 — 0.52) ~
1350
18.3565
18.3565, so the standard error is st.err. 2
2 0.0136 or 1.36%.
1350
This tells us that the percentage of support for Candidate B the day of
the poll was between 52 – 2 × 1.36 and 52+ 2×1.36, that is between 49.28%
and 54.72%.
When we plot these two intervals one on top the other we clearly see that
they overlap.
A
E**
*****I
45.28
48
50.72
В
E******:
******I
49.28
52
54.72
Overlap
E********I
49.28
50.72
Figure 4.18: Overlapping Confidence Intervals for Two Candidates
That means that with a 95% confidence level, we cannot say that one
candidate beats the other. We call this situation a statistical tie, or we say
Transcribed Image Text:Now to the numbers! Let's begin with Candidate A. We have the following numbers: sample size n = 1350, favorable voters k 648. Therefore p 648 0.48 or 48%, and o 2 1350 x 0.48 х (1 — 0.48) ~ 18.3565, so the 1350 18.3565 standard error is st.err. - a 0.0136 or 1.36%. 1350 CHAPTER 4. STATISTICS 153 This tells us that the percentage of support for Candidate A the day of the poll was between 48 – 2 × 1.36 and 48+2×1.36, that is between 45.28% and 50.72%. Similarly, for Candidate B we have n = 1350, favorable voters k 702. 702 Therefore p = — 0.52 or 52%, and o ~ y/1350 x 0.52 х (1 — 0.52) ~ 1350 18.3565 18.3565, so the standard error is st.err. 2 2 0.0136 or 1.36%. 1350 This tells us that the percentage of support for Candidate B the day of the poll was between 52 – 2 × 1.36 and 52+ 2×1.36, that is between 49.28% and 54.72%. When we plot these two intervals one on top the other we clearly see that they overlap. A E** *****I 45.28 48 50.72 В E******: ******I 49.28 52 54.72 Overlap E********I 49.28 50.72 Figure 4.18: Overlapping Confidence Intervals for Two Candidates That means that with a 95% confidence level, we cannot say that one candidate beats the other. We call this situation a statistical tie, or we say
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 5 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
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