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Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of o=10. We have taken a random sample of size n=42 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=74.5. 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 = 75, 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=42 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. S5 S6 S7 S1 74.5 72.7 76.3 71.5 S2 S3 S4 S8 S9 $10 S11 x S12 75% 75% 95% 95% lower upper lower upper limit limit limit limit 77.5 Generate Samples 75% confidence intervals 95% confidence intervals

Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of o=10. We have taken a random sample of size n=42 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=74.5. 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 = 75, 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=42 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. S5 S6 S7 S1 74.5 72.7 76.3 71.5 S2 S3 S4 S8 S9 $10 S11 x S12 75% 75% 95% 95% lower upper lower upper limit limit limit limit 77.5 Generate Samples 75% confidence intervals 95% confidence intervals

MATLAB: An Introduction with Applications
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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S14 $15 S16 S17 S18 S19 S20 69.0 H 81.0 69.0 H 81.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, u = 75? (b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 75? (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. The center of the 75% confidence interval for Sample 1 is 75, 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. We would expect to find more 75% confidence intervals that contain the population mean than 95% confidence X
Transcribed Image Text:S14 $15 S16 S17 S18 S19 S20 69.0 H 81.0 69.0 H 81.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, u = 75? (b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 75? (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. The center of the 75% confidence interval for Sample 1 is 75, 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. We would expect to find more 75% confidence intervals that contain the population mean than 95% confidence X
Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of o=10. We have taken a random sample of size n = 42 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 = 74.5. 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 u=75, 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=42 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 S1 74.5 72.7 76.3 71.5 77.5 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 x Generate Samples 75% confidence intervals 95% confidence intervals
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=10. We have taken a random sample of size n = 42 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 = 74.5. 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 u=75, 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=42 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 S1 74.5 72.7 76.3 71.5 77.5 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 x Generate Samples 75% confidence intervals 95% confidence intervals
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