Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of = 9. We have taken a random sample of size = 60 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 = 79.8. 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 95% confidence interval. Suppose that the true mean of the population is μ = 80, which shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size = 60 from this same population. (The 75% and 95% 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% 95% 95% lower upper lower upper limit limit limit limit 82.1 S1 79.8 78.5 81.1 77.5 S2 79.7 78.4 81.0 77.4 82.0 S3 79.8 78.5 81.1 77.5 82.1 S4 79.1 77.8 80.4 76.8 81.4 S5 81.8 80.5 83.1 79.5 84.1 S6 81.0 79.7 82.3 78.7 83.3 S7 79.3 78.0 80.6 77.0 81.6 S8 80.6 79.3 81.9 78.3 82.9 76.0 80.6 S9 78.3 77.0 79.6 S10 80.8| 79.5 82.1 78.5 83.1 $11 80.5 79.2 81.8 78.2 82.8 S12 78.1 76.8 S13 80.1 78.8 79.4 75.8 80.4 81.4 77.8 82.4 78.6 83.2 S14 80.9 79.6 82.2 S15 81.1| 79.8 82.4 78.8 83.4 S16 82.6 81.3 83.9 80.3 84.9 S17 80.2 78.9 81.5 77.9 82.5 S18 80.1 78.8 81.4 77.8 82.4 S19 80.8 79.5 82.1 78.5 83.1 S20 79.7 78.4 81.0 77.4 82.0 75.0 75% confidence intervals 85.0 75.0 95% confidence intervals 41! 85.0
Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of = 9. We have taken a random sample of size = 60 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 = 79.8. 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 95% confidence interval. Suppose that the true mean of the population is μ = 80, which shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size = 60 from this same population. (The 75% and 95% 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% 95% 95% lower upper lower upper limit limit limit limit 82.1 S1 79.8 78.5 81.1 77.5 S2 79.7 78.4 81.0 77.4 82.0 S3 79.8 78.5 81.1 77.5 82.1 S4 79.1 77.8 80.4 76.8 81.4 S5 81.8 80.5 83.1 79.5 84.1 S6 81.0 79.7 82.3 78.7 83.3 S7 79.3 78.0 80.6 77.0 81.6 S8 80.6 79.3 81.9 78.3 82.9 76.0 80.6 S9 78.3 77.0 79.6 S10 80.8| 79.5 82.1 78.5 83.1 $11 80.5 79.2 81.8 78.2 82.8 S12 78.1 76.8 S13 80.1 78.8 79.4 75.8 80.4 81.4 77.8 82.4 78.6 83.2 S14 80.9 79.6 82.2 S15 81.1| 79.8 82.4 78.8 83.4 S16 82.6 81.3 83.9 80.3 84.9 S17 80.2 78.9 81.5 77.9 82.5 S18 80.1 78.8 81.4 77.8 82.4 S19 80.8 79.5 82.1 78.5 83.1 S20 79.7 78.4 81.0 77.4 82.0 75.0 75% confidence intervals 85.0 75.0 95% confidence intervals 41! 85.0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 = 9. We have taken a
random sample of size = 60 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "52", etc.)
As shown in the table, the sample mean of Sample 1 is x = 79.8. 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 95% confidence interval. Suppose that the true mean of the population is μ = 80, 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 = 60 from this same population. (The 75% and 95% 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% 95% 95%
lower upper lower upper
limit limit limit limit
78.5 81.1 77.5 82.1
S1 79.8
S2 79.7 78.4
81.0 77.4 82.0
S3 79.8 78.5 81.1 77.5 82.1
S4 79.1 77.8
80.4 76.8
81.4
S5 81.8 80.5
83.1 79.5 84.1
S6 81.0 79.7 82.3 78.7 83.3
S7 79.3 78.0
80.6 77.0 81.6
S8 80.6 79.3 81.9 78.3 82.9
59 78.3 77.0
79.6 76.0 80.6
82.1
81.8 78.2
78.5 83.1
82.8
|S10|80.8| 79.5
S11|805| 79.2
S12 78.1 76.8
S13 80.1 78.8
S14 80.9 79.6
79.4 75.8 80.4
77.8 82.4
81.4
82.2
78.6 83.2
S15 81.1| 79.8
82.4 78.8 83.4
S16 82.6 81.3
83.9
80.3
84.9
S17 80.2 78.9
81.5
77.9 82.5
S18 80.1 78.8
81.4
77.8 82.4
82.1
78.5 83.1
S19 80.8 79.5
S20 79.7 78.4
81.0 77.4 82.0
X
75.0
75% confidence intervals
H
85.0 75.0
95% confidence intervals
H
85.0
Transcribed Image Text:(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 80?
(b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 80?
(c) Choose ALL that are true.
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.
We would expect to find more 75% confidence intervals that contain the population mean than 95% confidence
intervals that contain the population mean. Given a sample, a higher confidence level results in a narrower interval.
The center of the 75% confidence interval for Sample 1 is 80, because the center of any confidence interval for the
population mean must be the population mean.
All of the 95% confidence intervals should be the same as each other. Since they are not all the same, there must
have been errors due to rounding.
None of the choices above are true.
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