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S15 76.1 74.3 77.9 73.1 79.1 S16 75.4 73.6 77.2 72.4 78.4 S17 77.4 75.6 79.2 74.4 80.4 S18 76.3 74.5 78.1 73.3 79.3 $19 76.1 74.3 77.9 73.1 79.1 S20 76.2 74.4 78.0 73.2 79.2 69.0 81.0 69.0 81.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 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. There is nothing wrong with the fact that the 95% confidence intervals are different from each other. Each confidence interval depends on its sample, and different samples may give different confidence intervals. It is surprising that some 75% confidence intervals are different from other 75% confidence intervals. They should all be the same, as long as the samples are random samples from the same population. The center of the 75% confidence interval for Sample 1 is 75.8, because the center of a confidence interval for the population mean must be the sample mean. We would expect to find more 95% 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. None of the choices above are true.

S15 76.1 74.3 77.9 73.1 79.1 S16 75.4 73.6 77.2 72.4 78.4 S17 77.4 75.6 79.2 74.4 80.4 S18 76.3 74.5 78.1 73.3 79.3 $19 76.1 74.3 77.9 73.1 79.1 S20 76.2 74.4 78.0 73.2 79.2 69.0 81.0 69.0 81.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 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. There is nothing wrong with the fact that the 95% confidence intervals are different from each other. Each confidence interval depends on its sample, and different samples may give different confidence intervals. It is surprising that some 75% confidence intervals are different from other 75% confidence intervals. They should all be the same, as long as the samples are random samples from the same population. The center of the 75% confidence interval for Sample 1 is 75.8, because the center of a confidence interval for the population mean must be the sample mean. We would expect to find more 95% 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. None of the choices above are true.

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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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 = 75.8. 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 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 75.8 74.0 77.6 72.8 78.8 S2 74.2 72.4 76.0 71.2 77.2 S3 75.8 74.0 77.6 72.8 78.8 S4 77.4 75.6 79.2 74.4 80.4 S5 73.9 72.1 75.7 70.9 76.9 S6 74.9 73.1 76.7 71.9 77.9 S7 74.5 72.7 76.3 71.5 77.5 S8 77.5 75.7 79.3 74.5 80.5 S9 75.3 73.5 77.1 72.3 78.3 74.3 69.5 75.5 77.3 72.5 78.5 76.3 71.5 77.5 75.6 79.2 70.8 76.8 80.4 x 510 725 70.7 S11 755 73.7 S12 74.5 72.7 S13 73.8 72.0 S14 77.4 75.6 Continue 74.4 75% confidence intervals 95% confidence intervals Submit Assignment ?
Transcribed Image Text: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 = 75.8. 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 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 75.8 74.0 77.6 72.8 78.8 S2 74.2 72.4 76.0 71.2 77.2 S3 75.8 74.0 77.6 72.8 78.8 S4 77.4 75.6 79.2 74.4 80.4 S5 73.9 72.1 75.7 70.9 76.9 S6 74.9 73.1 76.7 71.9 77.9 S7 74.5 72.7 76.3 71.5 77.5 S8 77.5 75.7 79.3 74.5 80.5 S9 75.3 73.5 77.1 72.3 78.3 74.3 69.5 75.5 77.3 72.5 78.5 76.3 71.5 77.5 75.6 79.2 70.8 76.8 80.4 x 510 725 70.7 S11 755 73.7 S12 74.5 72.7 S13 73.8 72.0 S14 77.4 75.6 Continue 74.4 75% confidence intervals 95% confidence intervals Submit Assignment ?
S15 76.1 74.3 77.9 73.1 79.1 $16 75.4 73.6 77.2 72.4 78.4 S17 77.4 75.6 79.2 74.4 80.4 S18 76.3 74.5 78.1 73.3 79.3 S19 76.1 74.3 77.9 73.1 79.1 S20 76.2 74.4 78.0 73.2 79.2 1 H 69.0 81.0 69.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 75? 81.0 (b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 75? Continue (c) Choose ALL that are true. There is nothing wrong with the fact that the 95% confidence intervals are different from each other. Each confidence interval depends on its sample, and different samples may give different confidence intervals. It is surprising that some 75% confidence intervals are different from other 75% confidence intervals. They should all be the same, as long as the samples are random samples from the same population. The center of the 75% confidence interval for Sample 1 is 75.8, because the center of a confidence interval for the population mean must be the sample mean. We would expect to find more 95% 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. None of the choices above are true.
Transcribed Image Text:S15 76.1 74.3 77.9 73.1 79.1 $16 75.4 73.6 77.2 72.4 78.4 S17 77.4 75.6 79.2 74.4 80.4 S18 76.3 74.5 78.1 73.3 79.3 S19 76.1 74.3 77.9 73.1 79.1 S20 76.2 74.4 78.0 73.2 79.2 1 H 69.0 81.0 69.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 75? 81.0 (b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 75? Continue (c) Choose ALL that are true. There is nothing wrong with the fact that the 95% confidence intervals are different from each other. Each confidence interval depends on its sample, and different samples may give different confidence intervals. It is surprising that some 75% confidence intervals are different from other 75% confidence intervals. They should all be the same, as long as the samples are random samples from the same population. The center of the 75% confidence interval for Sample 1 is 75.8, because the center of a confidence interval for the population mean must be the sample mean. We would expect to find more 95% 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. None of the choices above are true.
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