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 populationmean 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 isshown 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% confidenceintervals 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 upperlimit limit limit limitS1 75.8 74.0 77.6 72.8 78.8S2 74.2 72.4 76.0 71.2 77.2S3 75.8 74.0 77.6 72.8 78.8S4 77.4 75.6 79.2 74.4 80.4S5 73.9 72.1 75.7 70.9 76.9S6 74.9 73.1 76.7 71.9 77.9S7 74.5 72.7 76.3 71.5 77.5S8 77.5 75.7 79.3 74.5 80.5S9 75.3 73.577.1 72.3 78.374.3 69.5 75.577.3 72.5 78.576.3 71.5 77.575.679.270.8 76.880.4x510 725 70.7S11 755 73.7S12 74.5 72.7S13 73.8 72.0S14 77.4 75.6Continue74.475% confidence intervals95% confidence intervalsSubmit Assignment? S15 76.1 74.3 77.9 73.1 79.1$16 75.4 73.6 77.2 72.4 78.4S17 77.4 75.6 79.2 74.4 80.4S18 76.3 74.5 78.1 73.379.3S19 76.1 74.377.973.1 79.1S20 76.2 74.478.0 73.2 79.21H69.081.0 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 confidenceinterval 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 shouldall 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 thepopulation mean must be the sample mean.We would expect to find more 95% confidence intervals that contain the population mean than 75% confidenceintervals that contain the population mean. Given a sample, a higher confidence level results in a wider interval.None of the choices above are true.

Introduction: It is required to consider the 75% and 95% confidence intervals for the question.

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.

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS