Suppos ✓ are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of 5. We have taken arandom sample of size = 10 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 = 99.3. 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 90% confidence interval. Suppose that the true mean of the population is = 100, which isshown on the displays for the confidence intervals.Press the "Generate Samples" button to simulate taking 19 more random samples of size 71 = 10 from this same population. (The 75% and 90% confidenceintervals 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 upperlimit limit limit limit51 99.3 97.5 101.1 96.7 101.952 99.5 97.7101.3 96.9 102.153 98.9 97.154 99.1 97.3100.7 96.3 101.5100.9 96.5 101.755 97.0 95.298.8 94.4 99.656 98.9 97.1 100.7 96.3 101.557 99.3 97.5 101.1 96.7 101.958 101.1 99.3 102.9 98.5 103.759 97.8 96.0 99.6 95.2 100.4|sio|101.1| 993 | 1029 | 833| 103.7|s11|1011| $9.3 | 1029 | 933| 103.7S12 97.8 96.0 99.6 95.2 100.4S13 98.9 97.1 100.7 96.3 101.5S14 100.6 98.8 102.4 98.0 103.2|515|100.8| 99.0 | 1026 | 932 | 103.4s16 101.2 99.4 103.0 98.6 103.8s17 102.2 100.4 104.0 99.6 104.8S18 101.1 99.3 102.9 98.5 103.7S19 99.9 98.1 101.7 97.3 102.5s20 100.3 98.5 102.1 97.7 102.994.075% confidence intervals106.0 94.090% confidence intervals106.0(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 100?(b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, = 100?(c) Choose ALL that are true.For some of the samples, the 75% confidence interval is included in the 90% confidence interval, while for othersamples, this is not the case.We would expect to find more 90% 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.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.Since Sample 19 and Sample 20 are drawn from the same population, the center of the 90% confidence interval forSample 19 must be the same as the center of the 90% confidence interval for Sample 20.None of the choices above are true.Expañol18

The objective is to infer, if each defined confidence intervals include the population mean value.…

Suppos ✓ are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of G=5. We have taken a random sample of size = 10 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 I=99.3. 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 = 100, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size = 10 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% 90% 90% 75% I lower upper lower upper limit limit limit limit 97.5 101.1 96.7 101.9 51 99.3 52 99.5 97.7 53 98.9 97.1 100.7 96.3 101.3 96.9 102.1 101.5 54 99.1 97.3 100.9 96.5 101.7 55 97.0 95.2 98.8 94.4 99.6 56 98.9 97.1 100.7 96.3 101.5 57 99.3 97.5 101.1 96.7 101.9 58 101.1 99.3 102.9 98.5 103.7 59 97.8 96.0 99.6 95.2 100.4 $10 101.1 99.3 102.9 98.5 103.7 sai 1011 593 |1029| 935 | 102.7 S12 97.8 96.0 99.6 95.2 100.4 S13 98.9 97.1 100.7 96.3 101.5 S14 100.6 98.8 1024 98.0 103.2 $15 100.8 99.0 102.6 98.2 103.4 S16 101.2 99.4 103.0 98.6 103.8 S17 102.2 100.4 104.0 99.6 104.8 S18 101.1 99.3 102.9 98.5 103.7 $19 99.9 98.1 101.7 97.3 102.5 s20 100.3 98.5 102.1 97.7 102.9 94.0 75% confidence intervals 106.0 94.0 90% confidence intervals 106.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 100? (b) How many of the 90% confidence intervals constructed from the 20 samples contain the population mean, μ = 100? x

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P