You have taken a random sample of size / = 42 from a normal population that has a population mean of U = /) and a population standard deviation of G = 10, Your sample, which is Sample 1 in the table below, has a mean of x = 77.4. (In the table, Sample 1 is written "$1", Sample 2 is written "$2", etc.) (a) Based on Sample 1, graph the 73% and 90%% confidence intervals for the population mean. Use 1.130 for the critical value for the 73% confidence interval, and use 1.960 for the critical value for the 93% 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, u = 75. 75% confidence interval 95% confidence interval 69.0 84.0 69 0 34.0 76.5 76 5 69.0 84.0 69.0 84.0 X 5 ? X 5 ? (b) Press the "Generate Samples" button below to simulate taking 19 more samples of size /=42 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% 95% 95% lower | upper |lower upper limit limit limit limit 75% confidence intervals 95% confidence intervals S1 77.4 ? ? 52 73.9 72.1 75.7 70.9 76.9 53 74.9 73.1 76.7 71.9 77.9 54 75.8 74.0 77.6 72.8 78.8 $5 74.6 72.8 76.4 71.6 77.6 56 72.6 70.8 74.4 69.6 75.6 57 74.2 72.4 76.0 71.2 17.2 58 73.8 72.0 75.6 70.8 76.8 59 77.5 7 79.3 74.5 80.5 510 75.3 73.5 77.1 72.3 78.3 511 76.1 74.3 77.9 73.1 79.1 HI IIIIII, II III 512 76.2 7 78.0 73.2 79.2 513 75.8 74.0 77.6 72.8 78.8 514 75.8 74.0 77.6 2.8 78.8 515 75.5 73.7 77.3 72.5 78.5 516 72.5 70.7 74.3 69.5 75.5 517 76.1 74.3 77.9 73.1 79.1 518 75.4 73.6 77.2 72.4 78.4 519 76.3 74.5 78.1 73.3 79.3 520 74.5 72.7 76.3 71.5 77.5 69.0 84.0 69.0 84.020 (c) Notice that for 50 = 100% of the samples, the 93% confidence interval contains the population mean. Choose the correct X 5 ? statement. O When constructing 90 % confidence intervals for 20 samples of the same size from the population, exactly 93 % of the samples must contain the population mean. There must have been an error with the way our samples were chosen. O 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 907, O When constructing 90 % confidence intervals for 20 samples of the same size from the population, at least 90% of the samples will contain the population mean. (d) Choose ALL that are true. O The 93% confidence interval for Sample 15 indicates that 90 %% of the Sample 15 data values are between 72.3 and 78.5. O The 75% confidence interval for Sample 15 is narrower than the 93% confidence interval for Sample 15. This must be the case, because when a confidence interval is constructed for a sample, the greater the level of confidence, the wider the confidence interval. O From the 75% confidence interval for Sample 15, we know that there is a 73% probability that the population mean is between 73.7 and 77.3. O If there were a Sample 21 of size /1 = 84 taken from the same population as Sample 15, then the 95% confidence interval for Sample 21 would be wider than the 93% confidence interval for Sample 15. O None of the choices above are true