Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of σ = 16. We have taken a random sample of size n = 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 x=58.9. 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 n = 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% x 75% 95% 95% lower upper lower upper limit limit limit limit S1 58.9 56.8 75% confidence intervals 95% confidence intervals 61.0 55.4 62.4 S2 59.3 57.2 61.4 55.8 62.8 S3 60.5 58.4 62.6 57.0 64.0 S4 61.1 59.0 63.2 57.6 64.6 S5 64.1 62.0 S6 58.5 56.4 66.2 60.6 67.6 60.6 55.0 62.0 S7 57.1 55.0 59.2 53.6 60.6 S8 57.2 55.1 59.3 53.7 60.7 S9 61.1 59.0 63.2 57.6 64.6 510 64.2 62.1 66.3 60.7 67.7 S11 59.8| 57.7 61.9 56.3 63.3 S12 58.9 56.8 61.0 55.4 62.4 S13 59.9 57.8 62.0 56.4 63.4 S14 62.7 60.6 64.8 59.2 66.2 S15 62.8| 60.7 S16 60.7 58.6 62.8 57.2 S17 61.1 59.0 63.2 S18 57.1 55.0 59.2 53.6 S19 60.3 58.2 62.4 S20 61.3 59.2 63.4 64.9 59.3 66.3 64.2 57.6 64.6 60.6 59.2 66.2 57.8 64.8 H 52.0 H++ 68.0 52.0 (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? 68.0 (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. 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. 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. 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. None of the choices above are true. G