Suppose we are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of 6=19. We have taken a random sample of size=85 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 -118.8. 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 -120, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size=85 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 118.8 116.4 121.2 114.8 122.9 $2 120.4 118.0 122.8 116.4 124.4 $3 121.8 119.4 124.2 117.8 125.8 S4 120.6 118.2 123.0 116.6 124.6 S5 124.8 122.4 127.2 120.8 128.8 $6 121.1 118.7 123.5 117.1 125.1 $7 122.0 119.6 124.4 118.0 126.0 S8 117.0 114.6 119.4 113.0 121.0 S9 118.8 116.4 121.2 114.8 122.8 $10 116.6 114.2 119.0 112.6 120.6 511 118.7 116.3 | 1211 1147|1227. $12 119.8 117.4 122.2 115.8 123.8 S13 121.4 119.0 123.8 117.4 125.4 $14 123.4 121.0 125.8 119.4 127.4 $15 119.9 117.5 122.3 115.9 124.0 $16 123.4 121.0 125.8 119.4 127.4 S17 119.8 117.4 122.1 115.7 123.8 S18 116.5 114.1 118.9 112.5 120.5 $19 118.9 116.5 121.3 114.9 122.9 $20 119.2 116.9 121.6 115.2 123.3 75% confidence intervals 95% confidence intervals Espaol 111.0 H 129.0 111.0 (a) How many of the 75% confidence intervals constructed from the 20 samples contain the population mean, -120? (b) How many of the 95% confidence intervals constructed from the 20 samples contain the population mean, -120? (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. 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 120, because the center of any confidence interval for the population mean must be the population mean. 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. H 129.0