Esp You are looking at a population and are interested in the proportion p that has a certain characteristic. Unknown to

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: Esp You Are Looking At A Population And Are Interested In The Proportion P That Has A Certain Characteristic Unknown To 1 (39.25 KiB) Viewed 25 times

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Esp 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 p0.22. You have taken a random sample of size n-88 from the population and found that the proportion of the sample that has the characteristic is p=0.16. 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 80% and 95% confidence intervals for the population proportion. Use 1.282 for the critical value for the 80% confidence interval, and use 1.960 for the critical value for the 95% 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, 0.22. 80% confidence interval 95% confidence interval 000 0.41 0.00 0.41 0.22 0.22 ********** 0.00 0.41 0.00 041 (b) Press the "Generate Samples" button below to simulate taking 19 more samples of size n-88 from the same population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table. 80% 80% 95% 95% lower upper lower upper limit limit limit limit 80% confidence intervals 95% confidence intervals $1 0.16 7 73 ? ? $2 0.22 0.16 0.28 0.13. 0.31 Explanation Check H+++
(b) Pressure "Generate Samples" button below to simulate taking 19 more samples of size x-88 from the same population. Notice that the confidence intervals for these samples are drawn automatically. Then complete parts (c) and (d) below the table. 80% 80% 95% 95% lower upper lower upper limit limit limit limit 80% confidence intervals 95% confidence intervals $1 0.16 ? ? ? ? $2 0.22 0.16 0.28 0.13. 0.31 $3 0.19 0.14 0,24 0.11 0.27 S4 0.30 0.24 0.36 0.20 0:40 S5 0.19 0.14 0.24 0.11 0.27 56 0.25 0.19 0.31 0.34 0.16 0.30 0.15 0.33 57 0.24 0.18 58 0.23 0.17 59 0.23 0.17 0.29 0.14 0.32 0.29 0.14 0.32 $10 0.22 0.16. 0.28 0.13 0.31 $11 0.19 0.14 0.24 0.11 0.27 $12 0.19 0.14 0.24 0.11 0.27 $13 0.26 0.20 0.32 0.17 0.35 $14 0.21 0.15 0.27 0.12 0.30 $15 0.16 0.11 0.21 0.08 0.24 $16 0.20 0.15 0.25 0.12 0.28 S17 0.22 0.16 0.28 0.13 0.31
20 100% of the samples, the 95% confidence interval contains the population proportion. Choose the 20 correct statement. When constructing 95% confidence intervals for 20 samples of the same size from the population, at least 95% of the samples will contain the population proportion. When constructing 95% confidence intervals for 20 samples of the same size from the population, exactly 95% of the samples must contain the population proportion. There must have been an error with the way our samples were chosen. When constructing 95% confidence intervals for 20 samples of the same size from the population, the percentage of the samples that contain the population proportion should be close to 95%, but it may not be exactly 95%. (d) Choose ALL that are true. To guarantee that a confidence interval will contain the population proportion, the level of confidence must match the sample proportion. For example, if pequals 0.35, then the 35% confidence interval will contain the population proportion. The 80% confidence interval for Sample 8 is narrower than the 95% confidence interval for Sample B. This is coincidence; when constructing a confidence interval for a sample, there is no relationship between the level of confidence and the width of the interval. From the 80% confidence interval for Sample 8, we cannot say that there is an 80% probability that the population proportion is between 0 and 0.41. If there were a Sample 21 of size 170 with the same sample proportion as Sample 8, then the 80% confidence interval for Sample 21 would be wider than the 80% confidence interval for Sample 8. None of the choices above are true. (c) Notice that for x