You are looking at a population and are interested in the proportion p that has a certain characteristic. Unknown to you, this population proportion is p = 0.65. ~ You have taken a random sample of size n = 105 from the population and found that the proportion of the sample that has the characteristic is p = 0.67. Your sample is Sample 1 in the table below. (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 proportion. 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 two decimal places. * For the points ( and #), enter the population proportion, 0.65. 75% confidence interval 90% confidence interval b 0.62 0.62 A bbb bbb bbb bbb b b e b e bbb b b e ] 0.49 0.82 0.49 0.82 (b) Press the "Generate Samples" button below to simulate taking 19 more samples of size / = 10) from the same 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% p lower upper lower upper 90% confidence intervals limit limit limit limit 75% confidence intervals $1 0.67 $2 0.64 0.59 0.69 0.56 0.72 0.66 0.61 0.71 0.58 0.74 0.66 0.61 0.71 0.58 0.74 0.64 0.59 0.69 0.56 0.72 $6 0.58 0.52 0.64 0.50 0.66 57 0.64 0.59 0.69 0.56 0.72 S8 0.58 0.52 0.64 0.50 0.66 $9 0.64 0.59 0.69 0.56 0.72 $10 0.66 0.61 0.71 0.58 0.74 S11 0.66 0.61 0.71 0.58 0.74 S12 0.58 0.52 0.64 0.50 0.66 S13 0.66 0.61 0.71 0.58 0.74 S14 0.71 0.66 0.76 0.64 0.78 $15 0.74 0.69 0.79 0.67 0.81 $16 0.63 0.58 0.68 0.55 0.71 $17 0.64 0.59 0.69 0.56 0.72 S18 0.74 0.69 0.79 0.67 0.81 S19 0.64 0.59 0.69 0.56 0.72 S20 0.65 0.60 0.70 0.57 0.73 0.49 0.82 0.49 0.8218 (c) Notice that for = 90% of the samples, the 90% confidence interval contains the population proportion. Choose the correct statement. ) When constructing 90% confidence intervals for 20 samples of the same size from the population, exactly 90% of the samples will contain the population proportion. ) 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 proportion. ) When constructing 90% confidence intervals for 20 samples of the same size from the population, it is possible that more or fewer than 90% of the samples will contain the population proportion. (d) Choose ALL that are true. [J] The 75% confidence interval for Sample 7 is narrower than the 90% confidence interval for Sample 7. This must be the case; when constructing a confidence interval for a sample, the greater the level of confidence, the wider the confidence interval. [J To guarantee that a confidence interval will contain the population proportion, the level of confidence must match the population proportion. For example, if p equals 0.49, then a 49% confidence interval will contain the population proportion. [ From the 90% confidence interval for Sample 7, we know that there is a 90% probability that the population proportion is between 0.49 and 0.82. [J If there were a Sample 21 of size n = 180 with the same sample proportion as Sample 7, then the 90% confidence interval for Sample 21 would be narrower than the 90% confidence interval for Sample 7. [J None of the choices above are true