Suppos ✓ are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of 16. We have taken arandom sample of size 72 = 80 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 = 61.1. 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 = 60, which isshown on the displays for the confidence intervals.Press the "Generate Samples" button to simulate taking 19 more random samples of size 71= 80 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 limit59.0 63.2 57.6 64.663.2 57.6 64.662.6 57.0 64.066.2 60.6 67.662.8 57.2 64.261.9 56.3 63.359.2 53.660.659.353.7 60.763.2 57.6 64.662.4 59.2 66.262.0 56.4 63.466.3 60.7 67.761.0 55.4 62.466.264.8 59.264.9 59.3 66.360.6 55.0 62.061.0 55.4 62.459.2 53.6 60.6$19 59.3 57.2 61.4 55.8 62.8520 61.3 59.2 63.4 57.8 64.8S1 61.152 61.1 59.053 60.5 58.454 64.1 62.055 60.7 58.656 59.8 57.757 57.1 55.0SB 57.2 55.159 61.159.0$10 60.3 58.2511 59.9 57.8S12 64.2 62.1513 58.9 56.8514 62.7 60.6$15 62.8 60.7516 58.5 56.4517 58.9 56.8S18 57.1 55.052.075% confidence intervals68.0 52.095% confidence intervals68.0(a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 60?(b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, μ = 60?(c) Choose ALL that are true.All of the 95% confidence intervals should be the same as each other. Since they are not all the same, there musthave been errors due to rounding.It is not surprising that some 75% confidence intervals are different from other 75% confidence intervals. Eachconfidence interval depends on its sample, and different samples may give different confidence intervals.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.The center of the 75% confidence interval for Sample 1 is 60, because the center of any confidence interval for thepopulation mean must be the population mean.None of the choices above are true.Expañol

The objective is to interpret the given confidence intervals with the confidence level of 95% and…

Suppos ✓ are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of 16. We have taken a random sample of size 10=80 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 = 61.1. 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 = 60, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size = 80 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 51 61.1 59.0 63.2 57.6 64.6 52 61.1 59.0 63.2 57.6 64.6 53 60.5 58.4 62.6 57.0 64.0 54 64.1 62.0 66.2 60.6 67.6 62.8 57.2 64.2 61.9 56.3 63.3 59.2 60.6 55 60.7 58.6 56 59.8 57.7 57 57.1 55.0 S8 57.2 55.1 59 61.1 59.0 510 60.3 58.2 53.6 59.3 53.7 60.7 63.2 57.6 64.6 62.4 59.2 66.2 511 59.9 57.8 62.0 56.4 63.4 66.3 60.7 67.7 55.4 62.4 512 64.2 62.1 513 58.9 56.8 S14 62.7 60.6 $15 62.8 60.7 61.0 64.8 59.2 66.2 64.9 59.3 66.3 S16 58.5 56.4 60.6 55.0 62.0 517 58.9 56.8 61.0 55.4 62.4 S18 57.1 55.0 59.2 53.6 60.6 $19 59.3 57.2 61.4 55.8 62.8 520 61.3 59.2 63.4 57.8 64.8 IM A 52.0 75% confidence intervals 68.0 52.0 95% confidence intervals 68.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, μ = 60? (b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, = 60? (c) Choose ALL that are true. 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. 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 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. The center of the 75% confidence interval for Sample 1 is 60, because the center of any confidence interval for the population mean must be the population mean. None of the choices above are true. G DE B>