Find the standard deviation for the sampling distribution of the sample proportion with (i) n=100 and (ii) n=1,000 . Explain why the sample proportion would be very likely (as the figure suggests) to fall (i) between 0.35 and 0.65 when n = 100 and (ii) between 0.45 and 0.55 when n = 1,000 (HINT: Recall that for an approximately normal distribution, nearly the entire distribution is within 3 standard deviations of the mean.) Explain how the results in part b indicate that the sample proportion tends to estimate the population proportion more precisely when the sample size is larger.
Find the standard deviation for the sampling distribution of the sample proportion with (i) n=100 and (ii) n=1,000 . Explain why the sample proportion would be very likely (as the figure suggests) to fall (i) between 0.35 and 0.65 when n = 100 and (ii) between 0.45 and 0.55 when n = 1,000 (HINT: Recall that for an approximately normal distribution, nearly the entire distribution is within 3 standard deviations of the mean.) Explain how the results in part b indicate that the sample proportion tends to estimate the population proportion more precisely when the sample size is larger.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Find the standard deviation for the sampling distribution of the sample proportion with (i)
n=100 and (ii) n=1,000
.
Explain why the sample proportion would be very likely (as the figure suggests) to fall (i) between 0.35 and 0.65 when n = 100 and (ii) between 0.45 and 0.55 when n = 1,000
(HINT: Recall that for an approximately
Explain how the results in part b indicate that the sample proportion tends to estimate the population proportion more precisely when the
.
Transcribed Image Text:7.10 EFFECT OF ʼn ON SAMPLE PROPORTION The figure illustrates
two sampling distributions for sample proportions when the population
proportion p = 0.50.
0.35 0.40 0.45
Population proportion
0.50
n = 1,000, showing sample
proportion very likely to
fall between 0.45 and 0.55
n = 100
0.55 0.60
0.65
Sample proportion
Expert Solution
Step 1
i)
Suppose p is the population proportion.
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman