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A simple random sample of size n is drawn. The sample mean, x, is found to be 17.7, and the sample standard deviation, s, is found to be 4.1. 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 34. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.)

A simple random sample of size n is drawn. The sample mean, x, is found to be 17.7, and the sample standard deviation, s, is found to be 4.1. 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 34. Lower bound: ; Upper bound: (Use ascending order. Round to two decimal places as needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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10/9/23, 10:40 AM df 4 5 SOUHABHS 25%28 58332 85838523355558 0.05 1.963 3.078 6.314 0.816 1.061 1.386 1.886 2.920 0.765 0.978 1.250 1.638 2.353 0.741 0.941 1.190 1.533 2.132 0.727 0.920 1.156 1.476 2.015 0.906 1.134 1.440 1.943 1.119 1.415 1.895 1.108 1.397 1.860 6 0.718 7 0.711 0.896 0.889 12.706 4.303 3.182 2.776 2.571 2.447 2.612 3.143 3.707 2.365 2.517 2.998 3.499 2.306 2.449 2.896 3.355 2.262 2.398 2.821 3.250 2.228 2.359 2.764 3.169 2.201 2.328 2.718 3.106 2.179 2.303 2.681 3.055 2.160 2.282 2.650 3.012 2.145 2.264 2.624 2.977 2.131 2.249 2.602 2.947 2.120 2.235 2.110 2.224 2.101 2.214 2.552 2.878 2.205 2.539 2.861 2.197 2.528 2.845 2.921 2.583 2.567 2.898 2.831 2.819 2.807 2.492 2.797 ervoo 8 0.706 9 0.703 0.883 1.100 1.383 1.833 10 0.700 0.879 1.093 1.372 1.812 11 0.697 0.876 1.088 1.363 1.796 12 0.695 0.873 1.083 1.356 1.782 13 0.694 0.870 1.079 1.350 1.771 14 0.692 0.868 1.076 1.345 1.761 15 0.691 0.866 1.074 1.341 1.753 16 0.690 0.865 1.071 1.337 1.746 17 0.689 0.863 1.069 1.333 1.740 18 0.688 0.862 1.067 1.330 1.734 19 0.688 0.861 1.066 1.328 1.729 2.093 20 0.687 0.860 1.064 1.325 1.725 2.086 21 0.686 0.859 1.063 1.323 1.721 2.080 22 0.686 0.858 1.061 1.321 1.717 2.074 0.685 0.858 1.060 1.319 1.714 2.069 24 0.685 0.857 1.059 1.318 1.711 2.064 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 26 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 27 0.684 0.855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 29 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 30 0.683 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 31 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 0.682 0.853 1.054 1.309 1.694 2.037 2.141 2.449 0.682 0.853 1.053 1.308 1.692 2.035 2.138 2.445 2.733 0.682 0.852 1.052 1.307 1.691 2.032 0.682 0.852 1.052 1.306 1.690 2.030 36 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 37 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 2.980 39 0.681 0.851 1.050 1.304 1.685 2.023 2.125 2.426 2.708 40 0.681 0.851 1.050 1.303 1.684 2.021 2.123 2.423 50 0.679 0.849 1.047 1.299 1.676 2.009 2.109 60 0.679 0.848 1.045 1.296 1.671 2.000 2.099 70 0.678 0.847 1.044 1.294 1.667 1.994 2.093 2.381 2.648 80 0.678 0.846 1.043 1.292 1.664 1.990 2.088 2.374 2.639 90 0.677 0.846 1.042 1.291 1.662 1.987 2.084 2.368 2.632 100 0.677 0.845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 1000 0.675 0.842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 Z 0.674 0.842 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.744 2.738 3.008 3.002 2.136 2.441 2.728 2.133 2.438 2.724 2.996 2.976 2.704 2.971 2.403 2.678 2.390 2.660 df 0.25 34 1 1.000 1.376 2 0.20 -Area in right tail 0.25 0.15 0.20 0.15 0.10 0.10 Table VI t-Distribution Area in Right Tail 0.025 0.05 0.025 0.02 0.01 2.189 2.518 2.183 2.508 2.177 2.500 2.172 2.167 0.02 15.894 31.821 4.849 6.965 3.482 4.541 5.841 2.999 3.747 4.604 2.757 3.365 4.032 Area in Right Tail Table of t-Distribution Areas 0.005 0.0025 0.0005 63.657 127.321 318.309 636.619 9.925 14.089 22.327 31.599 7.453 10.215 12.924 5.598 7.173 8.610 4.773 5.893 6.869 0.01 0.005 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.022 3.015 0.001 2.871 2.813 2.807 5.208 4.785 4.501 0.0025 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.067 3.435 3.057 3.421 3.047 3.038 3.030 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.408 3.396 3.385 3.375 3.365 3.356 3.348 3.340 3.333 3.326 3.319 2.937 2.915 2.899 2.887 3.195 2.878 3.183 3.313 3.307 3.261 3.232 3.211 3.174 3.098 3.090 0.001 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.633 3.622 3.611 3.601 3.591 3.582 3.574 3.566 3.558 3.551 3.496 3.460 3.435 3.416 3.402 3.390 3.300 3.291 0.0005 https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=661266309&questionId=49&flushed=false&cId=7616404&back-DoAssignments.aspx 1/1
Transcribed Image Text:10/9/23, 10:40 AM df 4 5 SOUHABHS 25%28 58332 85838523355558 0.05 1.963 3.078 6.314 0.816 1.061 1.386 1.886 2.920 0.765 0.978 1.250 1.638 2.353 0.741 0.941 1.190 1.533 2.132 0.727 0.920 1.156 1.476 2.015 0.906 1.134 1.440 1.943 1.119 1.415 1.895 1.108 1.397 1.860 6 0.718 7 0.711 0.896 0.889 12.706 4.303 3.182 2.776 2.571 2.447 2.612 3.143 3.707 2.365 2.517 2.998 3.499 2.306 2.449 2.896 3.355 2.262 2.398 2.821 3.250 2.228 2.359 2.764 3.169 2.201 2.328 2.718 3.106 2.179 2.303 2.681 3.055 2.160 2.282 2.650 3.012 2.145 2.264 2.624 2.977 2.131 2.249 2.602 2.947 2.120 2.235 2.110 2.224 2.101 2.214 2.552 2.878 2.205 2.539 2.861 2.197 2.528 2.845 2.921 2.583 2.567 2.898 2.831 2.819 2.807 2.492 2.797 ervoo 8 0.706 9 0.703 0.883 1.100 1.383 1.833 10 0.700 0.879 1.093 1.372 1.812 11 0.697 0.876 1.088 1.363 1.796 12 0.695 0.873 1.083 1.356 1.782 13 0.694 0.870 1.079 1.350 1.771 14 0.692 0.868 1.076 1.345 1.761 15 0.691 0.866 1.074 1.341 1.753 16 0.690 0.865 1.071 1.337 1.746 17 0.689 0.863 1.069 1.333 1.740 18 0.688 0.862 1.067 1.330 1.734 19 0.688 0.861 1.066 1.328 1.729 2.093 20 0.687 0.860 1.064 1.325 1.725 2.086 21 0.686 0.859 1.063 1.323 1.721 2.080 22 0.686 0.858 1.061 1.321 1.717 2.074 0.685 0.858 1.060 1.319 1.714 2.069 24 0.685 0.857 1.059 1.318 1.711 2.064 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 26 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 27 0.684 0.855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 29 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 30 0.683 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 31 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 0.682 0.853 1.054 1.309 1.694 2.037 2.141 2.449 0.682 0.853 1.053 1.308 1.692 2.035 2.138 2.445 2.733 0.682 0.852 1.052 1.307 1.691 2.032 0.682 0.852 1.052 1.306 1.690 2.030 36 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 37 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 2.980 39 0.681 0.851 1.050 1.304 1.685 2.023 2.125 2.426 2.708 40 0.681 0.851 1.050 1.303 1.684 2.021 2.123 2.423 50 0.679 0.849 1.047 1.299 1.676 2.009 2.109 60 0.679 0.848 1.045 1.296 1.671 2.000 2.099 70 0.678 0.847 1.044 1.294 1.667 1.994 2.093 2.381 2.648 80 0.678 0.846 1.043 1.292 1.664 1.990 2.088 2.374 2.639 90 0.677 0.846 1.042 1.291 1.662 1.987 2.084 2.368 2.632 100 0.677 0.845 1.042 1.290 1.660 1.984 2.081 2.364 2.626 1000 0.675 0.842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 Z 0.674 0.842 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.744 2.738 3.008 3.002 2.136 2.441 2.728 2.133 2.438 2.724 2.996 2.976 2.704 2.971 2.403 2.678 2.390 2.660 df 0.25 34 1 1.000 1.376 2 0.20 -Area in right tail 0.25 0.15 0.20 0.15 0.10 0.10 Table VI t-Distribution Area in Right Tail 0.025 0.05 0.025 0.02 0.01 2.189 2.518 2.183 2.508 2.177 2.500 2.172 2.167 0.02 15.894 31.821 4.849 6.965 3.482 4.541 5.841 2.999 3.747 4.604 2.757 3.365 4.032 Area in Right Tail Table of t-Distribution Areas 0.005 0.0025 0.0005 63.657 127.321 318.309 636.619 9.925 14.089 22.327 31.599 7.453 10.215 12.924 5.598 7.173 8.610 4.773 5.893 6.869 0.01 0.005 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.022 3.015 0.001 2.871 2.813 2.807 5.208 4.785 4.501 0.0025 4.297 4.144 4.025 3.930 3.852 3.787 3.733 3.686 3.646 3.610 3.067 3.435 3.057 3.421 3.047 3.038 3.030 3.579 3.552 3.527 3.505 3.485 3.467 3.450 3.408 3.396 3.385 3.375 3.365 3.356 3.348 3.340 3.333 3.326 3.319 2.937 2.915 2.899 2.887 3.195 2.878 3.183 3.313 3.307 3.261 3.232 3.211 3.174 3.098 3.090 0.001 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.633 3.622 3.611 3.601 3.591 3.582 3.574 3.566 3.558 3.551 3.496 3.460 3.435 3.416 3.402 3.390 3.300 3.291 0.0005 https://mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=661266309&questionId=49&flushed=false&cId=7616404&back-DoAssignments.aspx 1/1
A simple random sample of size n is drawn. The sample mean, x, is found to be 17.7, and the sample standard deviation, s, is found to be 4.1. 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 34. Lower bound:; Upper bound: (Use ascending order. Round to two decimal places as needed.)
Transcribed Image Text:A simple random sample of size n is drawn. The sample mean, x, is found to be 17.7, and the sample standard deviation, s, is found to be 4.1. 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 34. Lower bound:; Upper bound: (Use ascending order. Round to two decimal places as needed.)
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### Understanding Confidence Intervals and Margin of Error **Sample Overview:** A simple random sample of size \( n \) is drawn. The sample mean, \( \bar{x} \), is found to be 17.7, and the sample standard deviation, \( s \), is found to be 4.1. **Confidence Interval Construction:** - **(a)** For a sample size \( n = 34 \): - **95% Confidence Interval:** - Lower bound: 16.27 - Upper bound: 19.13 - Instruction: Use ascending order. Round to two decimal places as needed. - **(b)** For a sample size \( n = 61 \): - **95% Confidence Interval:** - Lower bound: 16.65 - Upper bound: 18.75 - Instruction: Use ascending order. Round to two decimal places as needed. **Effect of Sample Size on Margin of Error:** How does increasing the sample size affect the margin of error, \( E \)? - **Options:** - A. The margin of error increases. - B. The margin of error does not change. - C. The margin of error decreases. When the sample size increases, the margin of error typically decreases, making the confidence interval narrower. This indicates a more precise estimate of the population mean.
Transcribed Image Text:### Understanding Confidence Intervals and Margin of Error **Sample Overview:** A simple random sample of size \( n \) is drawn. The sample mean, \( \bar{x} \), is found to be 17.7, and the sample standard deviation, \( s \), is found to be 4.1. **Confidence Interval Construction:** - **(a)** For a sample size \( n = 34 \): - **95% Confidence Interval:** - Lower bound: 16.27 - Upper bound: 19.13 - Instruction: Use ascending order. Round to two decimal places as needed. - **(b)** For a sample size \( n = 61 \): - **95% Confidence Interval:** - Lower bound: 16.65 - Upper bound: 18.75 - Instruction: Use ascending order. Round to two decimal places as needed. **Effect of Sample Size on Margin of Error:** How does increasing the sample size affect the margin of error, \( E \)? - **Options:** - A. The margin of error increases. - B. The margin of error does not change. - C. The margin of error decreases. When the sample size increases, the margin of error typically decreases, making the confidence interval narrower. This indicates a more precise estimate of the population mean.
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Follow-up Question
A simple random sample of size n is drawn. The sample mean, x, is found to be 17.7, and the sample standard deviation, s, is found to be 4.1. 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 34. Lower bound: 16.27; Upper bound: 19.13 (Use ascending order. Round to two decimal places as needed.) (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.)
Transcribed Image Text:A simple random sample of size n is drawn. The sample mean, x, is found to be 17.7, and the sample standard deviation, s, is found to be 4.1. 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 34. Lower bound: 16.27; Upper bound: 19.13 (Use ascending order. Round to two decimal places as needed.) (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.)
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