A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10.

(a) Construct a 98% confidence interval about μ if the sample size, n, is
18.

Lower bound:___
Upper bound:____ (Use ascending order. Round to one decimal place as needed.)

(b) Construct a 98% confidence interval about μ if the sample size, n, is
29.

lower bound ___

upper bound___ (Use ascending order. Round to one decimal place as needed.)

(c) Construct a 99% confidence interval about μ if the sample size, n, is
18.

Lower bound ___

Upper bound___ (Use ascending order. Round to one decimal place as needed.)

(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
Transcribed Image Text:Table of t-Distribution Areas 318.309 22.327 10.215 7.173 1 1.000 1.376 1.061 0.978 1.963 1.386 1.250 1.190 1.156 3.078 1.886 1.638 1.533 1.476 6.314 12.706 4.303 3.182 15.894 31.821 63.657 127.321 636.619 6.965 4.541 3.747 3.365 0.816 2.920 2.353 2.132 2.015 4.849 3.482 2.999 2.757 9.925 5.841 4.604 4.032 14.089 7.453 5.598 4.773 31.599 12.924 3 0.765 4 0.741 0.941 2.776 8.610 6.869 5 0.727 0.920 2.571 5.893 0.718 0.711 2.612 2.517 0.906 1.134 1.440 1.943 2.447 2.365 2.306 2.262 3.143 3.707 4.317 5.208 4.785 5.959 5.408 5.041 4.781 0.896 2.998 1.415 1.895 1.108 1.397 1.860 1.383 1.372 1.119 2.449 2.398 2.359 3.499 3.355 3.250 3.169 4.029 3.833 3.690 4.501 4.297 8 0.706 0.703 0.700 0.889 0.883 0.879 2.896 2.821 9 1.100 1.833 10 1.093 1.812 2.228 2.764 3.581 4.144 4.587 2.201 2.179 2.160 2.145 3.497 3.428 3.372 4.025 3.930 3.852 3.787 3.733 0.876 0.873 11 1.088 0.697 0.695 1.363 1.356 1.350 1.345 1.341 1.796 2.328 2.303 2.718 3.106 3.055 3.012 2.977 2.947 4.437 4.318 4.221 1.782 2.681 2.650 12 1.083 1.079 13 2.282 2.264 2.249 0.694 0.870 1.771 14 0.692 1.076 1.761 2.624 3.326 3.286 4.140 4.073 0.868 15 0.691 0.866 1.074 1.753 2.131 2.602 2.120 2.110 2.101 2.235 2.224 2.583 2.567 2.552 2.539 2.528 0.690 1.071 1.069 1.337 2.921 2.898 3.252 4.015 3.965 16 0.865 0.863 0.862 1.746 3.686 3.646 3.610 3.579 3.552 17 0.689 0.688 0.688 0.687 1.333 1.740 3.222 3.197 3.174 3.153 3.922 3.883 3.850 2.878 2.861 18 1.067 1.330 1.734 2.214 1.066 1.064 19 0.861 1.328 1.729 2.093 2.205 20 0.860 1.325 1.725 2.086 2.197 2.845 1.063 1.061 1.060 1.323 1.721 1.321 2.518 2.508 2.500 2.492 2.485 21 0.686 0.859 2.080 2.189 2.831 3.135 3.119 3.104 3.091 3.078 3.527 3.819 0.858 0.858 2.183 2.177 2.172 22 2.074 3.792 0.686 0.685 0.685 1.717 2.819 3.505 3.485 1.714 23 24 1.319 1.318 2.069 2.064 2.060 2.807 3.768 0.857 0.856 1.059 1.711 2.797 3.467 3.745 25 0.684 1.058 1.316 1.708 2.167 2.787 3.450 3.725 2.162 2158. 3.067 3.435 3 421 26 0.856 0 85. 1.058 1.315 1.706 1 314. 1 703. 2.056 2.479 2 473. 2.779 2 771. 0.684 3.707 27 0 684 1 057 2052 3.057 3.690 Print Done parts remaining Clear All
Transcribed Image Text:i Table of t-Distribution Areas 2.056 1.315 1.314 3.067 3.057 3.047 3.038 26 0.856 2.779 0.684 0.684 1.058 1.057 1.056 1.055 1.055 1.706 2.162 2.479 3.435 3.707 0.855 0.855 0.854 27 1.703 2.052 2.158 2.154 2.150 2.147 2.473 2.771 3.421 3.408 3.396 3.385 3.690 28 29 0.683 0.683 0.683 1.313 1.311 1.701 1.699 2.048 2.045 2.042 2.467 2.462 2.457 2.763 2.756 3.674 3.659 30 0.854 1.310 1.697 2.750 3.030 3.646 1.054 1.054 1.053 1.052 1.052 3.375 3.365 3.356 3.348 3.340 0.682 1.309 1.696 2.744 2.738 2.733 2.728 2.724 31 32 0.853 2.040 2.144 2.141 2.138 2.136 2.133 2.453 2.449 3.022 3.633 3.622 3.611 1.694 1.692 1.691 1.690 3.015 3.008 3.002 2.996 0.853 1.309 2.037 0.682 0.682 33 34 0.853 0.852 1.308 1.307 2.035 2.032 2.030 2.445 2.441 2.438 0.682 3.601 35 0.682 0.852 1.306 3.591 2.028 2.026 36 0.852 1.052 1.306 1.305 1.304 2.131 3.333 3.326 3.319 3.313 3.307 3.582 3.574 3.566 0.681 1.688 2.434 2.431 2.719 2.990 2.985 37 38 39 2.715 2.712 2.708 0.681 0.851 0.851 0.851 1.051 1.051 1.050 1.687 2.129 1.686 1.685 1.684 2.127 2.125 2.123 0.681 2.024 2.429 2.426 2.980 2.976 2.971 2.023 3.558 3.551 0.681 1.304 40 0.681 0.851 1.050 1.303 2.021 2.423 2.704 2.937 2.915 3.496 3.460 3.435 3.416 0.679 0.679 0.849 1.047 1.676 2.009 2.000 1.994 2.678 50 60 1.299 1.296 2.109 2.099 2.093 2.088 2.084 3.261 3.232 3.211 2.403 2.390 1.045 1.044 0.848 1.671 2.660 70 0.678 0.847 1.294 1.667 2.381 2.648 2.639 2.632 2.899 1.043 1.042 2.887 80 90 0.678 0.677 1.664 1.662 3.195 3.183 0.846 1.292 1.291 1.990 2.374 2.368 0.846 1.987 2.878 3.402 1.042 1.037 1.290 1.282 1.282 2.626 2.581 2.576 100 0.677 0.845 0.842 0.842 1.660 1.984 1.962 1.960 2.081 2.056 2.054 2.364 2.871 2.813 2.807 3.174 3.390 1000 0.675 1.646 2.330 3.098 3.300 0.674 1.036 1.645 2.326 3.090 3.291 df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 Area in Right Tail Print Done parts remaining Clear All

Name: A simple random sample of size n is drawn from a population that is no
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Description: A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10. (a) Construct a 98% confidence interval about μ if the s

Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10.

(a) Construct a 98% confidence interval about μ if the sample size, n, is

18.

Lower bound:___
Upper bound:____ (Use ascending order. Round to one decimal place as needed.)

(b) Construct a 98% confidence interval about μ if the sample size, n, is

29.

lower bound ___

upper bound___ (Use ascending order. Round to one decimal place as needed.)

(c) Construct a 99% confidence interval about μ if the sample size, n, is

18.

Lower bound ___

Upper bound___ (Use ascending order. Round to one decimal place as needed.)

(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?