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9. A simple random sample of size n is drawn. The sample mean, x, is found to be 18.3, and the sample standard deviation, s, is found to be 4.8. 15 Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about u if the sample size, n, is 35. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 61. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E?

9. A simple random sample of size n is drawn. The sample mean, x, is found to be 18.3, and the sample standard deviation, s, is found to be 4.8. 15 Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about u if the sample size, n, is 35. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about u if the sample size, n, is 61. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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9. A simple random sample of size n is drawn. The sample mean, x, is found to be 18.3, and the sample standard deviation, s, is found to be 4.8. 15 Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about µ if the sample size, n, is 35. ; Upper bound: (Use ascending order. Round to two decimal places as needed.) Lower bound: (b) Construct a 95% confidence interval about µ if the sample size, n, is 61. Lower bound: Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error decreases. O B. The margin of error does not change. C. The margin of error increases. (c) Construct a 99% confidence interval about u if the sample size, n, is 35. ; Upper bound: (Use ascending order. Round to two decimal places as needed.) Lower bound: Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. The margin of error increases. O B. The margin of error decreases. C. The margin of error does not change. (d) If the sample size is 12, what conditions must be satisfied to compute the confidence interval? O A. The sample must come from a population that is normally distributed and the sample size must be large. B. The sample data must come from a population that is normally distributed with no outliers. O C. The sample size must be large and the sample should not have any outliers.
Transcribed Image Text:9. A simple random sample of size n is drawn. The sample mean, x, is found to be 18.3, and the sample standard deviation, s, is found to be 4.8. 15 Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about µ if the sample size, n, is 35. ; Upper bound: (Use ascending order. Round to two decimal places as needed.) Lower bound: (b) Construct a 95% confidence interval about µ if the sample size, n, is 61. Lower bound: Upper bound: (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error decreases. O B. The margin of error does not change. C. The margin of error increases. (c) Construct a 99% confidence interval about u if the sample size, n, is 35. ; Upper bound: (Use ascending order. Round to two decimal places as needed.) Lower bound: Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E? O A. The margin of error increases. O B. The margin of error decreases. C. The margin of error does not change. (d) If the sample size is 12, what conditions must be satisfied to compute the confidence interval? O A. The sample must come from a population that is normally distributed and the sample size must be large. B. The sample data must come from a population that is normally distributed with no outliers. O C. The sample size must be large and the sample should not have any outliers.
Area in right tail Table VI t-Distribution Area in Right Tail 0.25 https://xlitemprod.pearsoncmg.com/api/v1/print/highered df 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 24/28 11/17/21,9:38 AM HW 9.2 (13 Quest)-Shams Ismael 3.078 1.886 1.376 1.061 0.978 0.941 1 1.000 1.963 6.314 12.706 15.894 31.821 63.657 127.321 318.30 9.925 5.841 4.604 22.32 0.816 0.765 4 6.965 4.541 3.747 3.365 14.089 1.386 1.250 1.190 2.920 4.303 4.849 1.638 1.533 2.353 2.132 2.015 3.182 2.776 3.482 2.999 7.453 10.21 0.741 5.598 4.773 7.17 5.89 0.727 0.920 1.156 1.476 2.571 2.757 4.032 0.718 2.612 3.143 2.998 2.896 2.821 2.764 6. 7 0.711 0.906 1.134 1.119 1.108 1.100 1.093 1.440 1.415 1.397 1.943 2.447 2.365 3.707 3.499 3.355 3.250 3.169 4.317 4.029 3.833 3.690 3.581 5.20 0.896 0.889 0.883 1.895 1.860 1.833 1.812 4.78 4.50 4.29 4.14 2.517 8 0.706 9. 0.703 0.700 1.383 1.372 2.306 2.262 2.228 2.449 2.398 2.359 10 0.879 3.497 3.428 11 1.088 4.02 0.697 0.695 0.694 0.692 0.691 0.876 1.363 1.796 2.201 2.328 2.718 3.106 1.356 1.350 0.873 1.782 1.771 1.761 1.753 2.681 12 13 1.083 2.179 2.303 3.055 3.93 1.079 1.076 3.85 3.78 3.73 0.870 2.160 2.282 2.650 3.012 2.977 3.372 0.868 0.866 14 1.345 1.341 2.145 2.131 2.264 2.624 3.326 15 1.074 2.249 2.602 2.947 3.286 0.690 0.689 0.688 2.921 2.898 2.878 3.252 3.222 0.865 1.337 2.120 2.235 2.224 2.214 2.205 2.197 2.583 2.567 2.552 16 3.68 1.071 1.069 1.067 1.066 1.746 17 0.863 1.333 1.740 2.110 3.64 3.61 3.57 3.55 1.734 1.729 2.101 2.093 18 0.862 1.330 1.328 1.325 3.197 0.688 0.687 3.174 3.153 19 0.861 2.539 2.861 20 0.860 1.064 1.725 2.086 2.528 2.845 1.063 1.061 1.721 1.717 2.189 2.183 2.177 2.172 2.518 2.508 2.831 2.819 2.807 2.797 2.787 21 0.686 0.859 1.323 1.321 1.319 2.080 2.074 3.135 3.119 3.104 3.091 3.078 3.52 3.50 3.48 3.46 3.45 22 0.686 23 24 25 0.685 0.685 0.684 0.858 0.858 0.857 0.856 1.060 1.714 2.069 2.500 1.059 1.058 1.318 1.316 1.711 2.064 2.492 1.708 2.060 2.167 2.485 0.856 0.855 0.855 1.058 1.057 1.056 1.055 1.055 1.315 1.314 2.162 2.158 2.779 2.771 26 0.684 0.684 1.706 2.056 2.052 2.479 2.473 3.067 3.43 1.703 1.701 3.057 3.047 3.038 27 3.42 0.683 0.683 2.154 2.150 2.467 2.462 2.763 2.756 28 1.313 2.048 2.045 2.042 3.40 3.39 3.38 29 0.854 0.854 1.311 1.699 30 0.683 1.310 1.697 2.147 2.457 2.750 3.030 1.309 1.309 1.308 2.453 2.449 2.445 2.441 2.438 2.744 2.738 2.733 2.728 2.724 3.022 3.015 3.008 3.002 2.996 31 0.682 0.853 0.853 1.054 1.054 1.053 1.052 1.052 1.696 2.040 2.144 1.694 1.692 1.691 2.037 2.035 2.032 2.030 3.37 3.36 3.35 3.34 3.34 32 33 0.682 0.682 2.141 2.138 0.853 0.852 0.852 1.307 1.306 34 0.682 2.136 35 0.682 1.690 2.133 1.052 1.051 1.051 1.050 36 0.681 0.852 2.028 2.434 1.306 1.305 1.304 1.688 1.687 2.131 2.719 2.990 2.985 2.980 3.33 3.32 3.31 3.31. 3.30 37 0.681 0.851 2.026 2.129 2.431 2.715 2.024 0.681 0.681 0.681 38 0.851 2.127 2.429 2.712 1.686 1.685 39 0.851 1.304 1.303 2.023 2.021 2.125 2.426 2.708 2.976 2.971 40 0.851 1.050 1.684 2.123 2.423 2.704 0.849 0.848 0.847 1.047 1.045 1.044 1.043 1.299 2.678 2.660 2.648 2.639 2.632 50 0.679 1.676 2.009 2.109 2.099 2.093 2.088 2.403 2.937 2.915 3.26 60 0.679 1.296 1.671 2.000 2.390 3.23 1.994 70 80 0.678 0.678 1.294 1.292 1.667 1.664 3.21 3.19 3.18 2.381 1.990 1.987 2.374 2.368 2.899 2.887 2.878 0.846 90 0.677 0.846 1.042 1.291 1.662 2.084 1.660 1.646 100 0.677 0.675 0.845 0.842 1.290 1.984 1.962 1.960 2.081 2.364 2.871 2.813 2.807 1.042 2.626 3.17 3.09 3.09 1.037 2.056 2.054 2.330 2.326 2.581 2.576 1000 1.282 1.282 0.674 0.842 1.036 1.645 df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 Area in Right Tail
Transcribed Image Text:Area in right tail Table VI t-Distribution Area in Right Tail 0.25 https://xlitemprod.pearsoncmg.com/api/v1/print/highered df 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 24/28 11/17/21,9:38 AM HW 9.2 (13 Quest)-Shams Ismael 3.078 1.886 1.376 1.061 0.978 0.941 1 1.000 1.963 6.314 12.706 15.894 31.821 63.657 127.321 318.30 9.925 5.841 4.604 22.32 0.816 0.765 4 6.965 4.541 3.747 3.365 14.089 1.386 1.250 1.190 2.920 4.303 4.849 1.638 1.533 2.353 2.132 2.015 3.182 2.776 3.482 2.999 7.453 10.21 0.741 5.598 4.773 7.17 5.89 0.727 0.920 1.156 1.476 2.571 2.757 4.032 0.718 2.612 3.143 2.998 2.896 2.821 2.764 6. 7 0.711 0.906 1.134 1.119 1.108 1.100 1.093 1.440 1.415 1.397 1.943 2.447 2.365 3.707 3.499 3.355 3.250 3.169 4.317 4.029 3.833 3.690 3.581 5.20 0.896 0.889 0.883 1.895 1.860 1.833 1.812 4.78 4.50 4.29 4.14 2.517 8 0.706 9. 0.703 0.700 1.383 1.372 2.306 2.262 2.228 2.449 2.398 2.359 10 0.879 3.497 3.428 11 1.088 4.02 0.697 0.695 0.694 0.692 0.691 0.876 1.363 1.796 2.201 2.328 2.718 3.106 1.356 1.350 0.873 1.782 1.771 1.761 1.753 2.681 12 13 1.083 2.179 2.303 3.055 3.93 1.079 1.076 3.85 3.78 3.73 0.870 2.160 2.282 2.650 3.012 2.977 3.372 0.868 0.866 14 1.345 1.341 2.145 2.131 2.264 2.624 3.326 15 1.074 2.249 2.602 2.947 3.286 0.690 0.689 0.688 2.921 2.898 2.878 3.252 3.222 0.865 1.337 2.120 2.235 2.224 2.214 2.205 2.197 2.583 2.567 2.552 16 3.68 1.071 1.069 1.067 1.066 1.746 17 0.863 1.333 1.740 2.110 3.64 3.61 3.57 3.55 1.734 1.729 2.101 2.093 18 0.862 1.330 1.328 1.325 3.197 0.688 0.687 3.174 3.153 19 0.861 2.539 2.861 20 0.860 1.064 1.725 2.086 2.528 2.845 1.063 1.061 1.721 1.717 2.189 2.183 2.177 2.172 2.518 2.508 2.831 2.819 2.807 2.797 2.787 21 0.686 0.859 1.323 1.321 1.319 2.080 2.074 3.135 3.119 3.104 3.091 3.078 3.52 3.50 3.48 3.46 3.45 22 0.686 23 24 25 0.685 0.685 0.684 0.858 0.858 0.857 0.856 1.060 1.714 2.069 2.500 1.059 1.058 1.318 1.316 1.711 2.064 2.492 1.708 2.060 2.167 2.485 0.856 0.855 0.855 1.058 1.057 1.056 1.055 1.055 1.315 1.314 2.162 2.158 2.779 2.771 26 0.684 0.684 1.706 2.056 2.052 2.479 2.473 3.067 3.43 1.703 1.701 3.057 3.047 3.038 27 3.42 0.683 0.683 2.154 2.150 2.467 2.462 2.763 2.756 28 1.313 2.048 2.045 2.042 3.40 3.39 3.38 29 0.854 0.854 1.311 1.699 30 0.683 1.310 1.697 2.147 2.457 2.750 3.030 1.309 1.309 1.308 2.453 2.449 2.445 2.441 2.438 2.744 2.738 2.733 2.728 2.724 3.022 3.015 3.008 3.002 2.996 31 0.682 0.853 0.853 1.054 1.054 1.053 1.052 1.052 1.696 2.040 2.144 1.694 1.692 1.691 2.037 2.035 2.032 2.030 3.37 3.36 3.35 3.34 3.34 32 33 0.682 0.682 2.141 2.138 0.853 0.852 0.852 1.307 1.306 34 0.682 2.136 35 0.682 1.690 2.133 1.052 1.051 1.051 1.050 36 0.681 0.852 2.028 2.434 1.306 1.305 1.304 1.688 1.687 2.131 2.719 2.990 2.985 2.980 3.33 3.32 3.31 3.31. 3.30 37 0.681 0.851 2.026 2.129 2.431 2.715 2.024 0.681 0.681 0.681 38 0.851 2.127 2.429 2.712 1.686 1.685 39 0.851 1.304 1.303 2.023 2.021 2.125 2.426 2.708 2.976 2.971 40 0.851 1.050 1.684 2.123 2.423 2.704 0.849 0.848 0.847 1.047 1.045 1.044 1.043 1.299 2.678 2.660 2.648 2.639 2.632 50 0.679 1.676 2.009 2.109 2.099 2.093 2.088 2.403 2.937 2.915 3.26 60 0.679 1.296 1.671 2.000 2.390 3.23 1.994 70 80 0.678 0.678 1.294 1.292 1.667 1.664 3.21 3.19 3.18 2.381 1.990 1.987 2.374 2.368 2.899 2.887 2.878 0.846 90 0.677 0.846 1.042 1.291 1.662 2.084 1.660 1.646 100 0.677 0.675 0.845 0.842 1.290 1.984 1.962 1.960 2.081 2.364 2.871 2.813 2.807 1.042 2.626 3.17 3.09 3.09 1.037 2.056 2.054 2.330 2.326 2.581 2.576 1000 1.282 1.282 0.674 0.842 1.036 1.645 df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 Area in Right Tail
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