You have taken a random sample of size 19 from a normal population that has a population mean of -50 and a population standard deviation of a=15. Your sample, which is Sample 1 in the table below, has a mean of 45.2. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) (a) Based on Sample 1, graph the 75% and 90% confidence intervals for the population mean. Use 1.150 for the critical value for the 75% confidence interval, and use 1.645 for the critical value for the 90% confidence interval. (If necessary, consult a list of formulas.) Enter the lower and upper limits on the graphs to show each confidence interval. Write your answers with one decimal place. For the points (and), enter the population mean, =50. 75% confidence interval 34.0 34.0 34.0 34.0 48.5 90% confidence interval 48.5 63.0 63.0 63.0 63.0 (b) Press the "Generate Samples" button below to simulate taking 19 more samples of size -19 from the population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table. 75% 75% 90% 90% lower upper lower upper limit limit limit limit ? ? 75% confidence intervals 41.5 52.9 S1 45.2 ? S2 47.2 43.2 53 48.4 44.4 S4 43.3 39.3 S5 47.2 43.2 S6 47.7 43.7 $7 43.4 39.4 S8 47.7 43.7 S9 56.5 52.5 510 524 SAI 488 448 S12 43.5 39.5 S13 51.3 47.3 51.2 52.4 42.7 54.1 47.3 37.6 49.0 51.2 41.5 52.9 51.7 42.0 53.4 47.4 37.7 49.1 51.7 42.0 53.4 60.5 50.8 62.2 56.4 46.7 58.1 52.8 43.1 54.5 47.5 37.8 49.2 55.3 45.6 57.0 S14 51.7 47.7 55.7 46.0 57.4 515 182 44.2 S16 52.3 48.3 S17 45.3 41.3 S18 54.7 50.7 S19 49.2 45.2 52.2 42.5 53.9 56.3 46.6 58.0 49.3 39.6 51.0 58.7 49.0 60.4 53.2 43.5 54.9 90% confidence intervals 63.0 34.0 63.0 S20 51.6 47.6 55.6 45.9 57.3 16 34.0 (c) Notice that for 100-80% of the samples, the 90% confidence interval contains the population mean. Choose the correct statement. When constructing 90% confidence intervals for 20 samples of the same size from the population, at most 90% of the samples will contain the population mean. When constructing 90% confidence intervals for 20 samples of the same size from the population, exactly 90% of the samples must contain the population mean. There must have been an error with the way our samples were chosen. When constructing 90% confidence intervals for 20 samples of the same size from the population, the percentage of the samples that contain the population mean should be close to 90%, but it may not be exactly 90%.