Homework Statistics 9.2

Pri 3. Determine the point estimate of the population mean and margin of error for the confidence interval. Lower bound is 19, upper bound is 31. The point estimate of the population mean is 25 The margin of error for the confidence interval is 6 4. A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 109, and the sample standard deviation, s, is found to be 10. a) Construct an 80% confidence interval about u if the sample size, n, is 28. b) Construct an 80% confidence interval about u if the sample size, n, is 23. (c) Construct a 70% confidence interval about u if the sample size, n, is 28. d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Click the icon to view the table of areas under the t-distribution. (a) Construct an 80% confidence interval about u if the sample size, n, is 28. Lower bound: ; Upper bound: (Use ascending order. Round to one decimal place as needed.) (b) Construct an 80% confidence interval about u if the sample size, n, is 23. Lower bound: ; Upper bound: Use ascending order. Round to one decimal place as needed.) How does decreasing the sample size affect the margin of error, E? O A. As the sample size decreases, the margin of error decreases. O B. As the sample size decreases, the margin of error stays the same. O C. As the sample size decreases, the margin of error increases (c) Construct a 70% confidence interval about u if the sample size, n, is 28. Lower bound: ; Upper bound: (Use ascending order. Round to one decimal place as needed.) Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? O A. As the level of confidence decreases, the size of the interval increases. O B. As the level of confidence decreases, the size of the interval decreases. O C. As the level of confidence decreases, the size of the interval stays the same. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? O A. No, the population needs to be normally distributed. O B. No, the population does not need to be normally distributed. O C. Yes, the population needs to be normally distributed. O D. Yes, the population does not need to be normally distributed. 2: Table of t-Distribution Areas - Area in right tail Table VI t-Distribution Area in Right Tail if 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1.000 1.376 1.963 3.078 6.314 12.706 15.894 31.821 63.657 127.321 318.309 636.619 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.089 22.327 31.599 0.765 0.978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 MAWNE 10.215 12.924 0.741 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610 0.727 0.920 1.156 1.476 2.015 2.571 2.757 3.365 4.032 4.773 5.893 6.869 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 5.959 0.711 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 0.700 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 11 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.106 3.497 4.025 4.437 12 0.695 0.873 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 13 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 14 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 15 0.691 0.866 1.074 1.341 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 16 0.690 0.865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 17 0.689 0.863 1.069 1.333 1.740 2.110 2.224 2.567 2.898 3.222 3.646 3.965 18 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.610 3.922 19 0.688 0.861 1.066 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 20 0.687 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 0.686 0.859 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 3.505 3.792 0.685 0.858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768 24 0.685 0.857 1.059 1.318 1.711 2.064 2.172 2.492 2.79 3.091 3.467 3.745 25 0.684 0.856 1.058 1.316 1.708 2.060 2.167 2.485 2.787 3.078 3.450 3.725 26 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 0.684 0.855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 3.690 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 3.038 3.396 3.659 30 0.683 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.030 3.385 3.646 31 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 2.744 3.022 3.375 3.633 32 0.682 0.853 1.054 1.309 1.694 2.037 2.141 2.449 2.738 3.015 3.365 3.622 0.682 0.853 1.053 1.308 1.692 2.035 2.138 2.445 2.733 3.008 3.356 3.611 34 0.682 0.852 1.052 1.307 1.691 2.032 2.136 2.441 2.728 3.002 3.348 3.601 35 0.682 0.852 1.052 1.306 1.690 2.030 2.133 2.438 2.724 2.996 3.340 3.591 36 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 3.333 3.582 37 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 3.326 3.574 38 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 2.980 3.319 3.566