(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, H= 50?| (b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, u=50? (c) Choose ALL that are true. O For some of the samples, the 75% confidence interval is included in the 90% confidence interval, while for other samples, this is not the case. O We would expect to find more 90% confidence intervals that contain the population mean than 75% confidence intervals that contain the population mean. Given a sample, a higher confidence level results in a wider interval. O It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each confidence interval depends on its sample, and different samples may give different confidence intervals. O Since Sample 19 and Sample 20 are drawn from the same population, the center of the 90% confidence interval for Sample 19 must be the same as the center of the 90% confidence interval for Sample 20. O None of the choices above are true.
(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, H= 50?| (b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, u=50? (c) Choose ALL that are true. O For some of the samples, the 75% confidence interval is included in the 90% confidence interval, while for other samples, this is not the case. O We would expect to find more 90% confidence intervals that contain the population mean than 75% confidence intervals that contain the population mean. Given a sample, a higher confidence level results in a wider interval. O It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each confidence interval depends on its sample, and different samples may give different confidence intervals. O Since Sample 19 and Sample 20 are drawn from the same population, the center of the 90% confidence interval for Sample 19 must be the same as the center of the 90% confidence interval for Sample 20. O None of the choices above are true.
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
Transcribed Image Text:(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, u= 50?||
(b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean,u=50? ||
(c) Choose ALL that are true.
O For some of the samples, the 75% confidence interval is included in the 90% confidence interval, while for other samples,
this is not the case.
O We would expect to find more 90% confidence intervals that contain the population mean than 75% confidence intervals
that contain the population mean. Given a sample, a higher confidence level results in a wider interval.
O It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Each
confidence interval depends on its sample, and different samples may give different confidence intervals.
O Since Sample 19 and Sample 20 are drawn from the same population, the center of the 90% confidence interval for
Sample 19 must be the same as the center of the 90% confidence interval for Sample 20.
O None of the choices above are true.
Transcribed Image Text:Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of o = 15. We have taken a
random sample of size n=19 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.)
As shown in the table, the sample mean of Sample 1 is x= 492. Also shown are the lower and upper limits of the 75% confidence interval for the population
mean using this sample, as well as the lower and upper limits of the 90% confidence interval. Suppose that the true mean of the population is µ= 50, which is
shown on the displays for the confidence intervals.
Press the "Generate Samples" button to simulate taking 19 more random samples of size n=19 from this same population. (The 75% and 90% confidence
intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table.
75% 75%
90%
90%
lower upper lower upper
limit
ar
limit
limit
limit
75% confidence intervals
90% confidence intervals
s1 49.2 45.2
53.2
43.5
54.9
S2 47.2 43.2
51.2
41.5
52.9
S3 51.3
47.3
55.3
45.6
57.0
S4 43.3 39.3
47.3
37.6
49.0
S5
52.4
48.4
56.4
46.7
58.1
S6 52.3
48.3
56.3
46.6
58.0
S7 43.4 39.4
47.4
37.7
49.1
S8 56.5 52.5
60.5
50.8
62.2
S9 48.2
44.2
52.2
42.5
53.9
s10 43.5
39.5
47.5
37.8
49.2
S11 48.4
44.4
52.4
42.7
54.1
S12 47.7
43.7
51.7
42.0
53.4
S13 45.2
41.2
49.2
39.5
50.9
S14 51.7
47.7
55.7
46.0
57.4
S15 45.3
41.3
49.3
39.6
51.0
S16 51.6 47.6
55.6
45.9
57.3
S17 47.7
43.7
51.7
42.0
53.4
S18 54.7
50.7
58.7
49.0
60.4
S19 48.8
44.8
52.8
43.1
54.5
S20 47.2
43.2
51.2
41.5
52.9
37.0
63.0 37.0
63.0
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 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