The method of tree-ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately nomal distribution. 1,306 1,278 1,278 1,208 1,268 1,316 1,275 1,317 1,275 LA USE SALT (3) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to four decimal places.) X A.D. YT (b) Find a 90%% confidence Interval for the mean of all tree-ring dates from this archaeological site. (Round your answers to the nearest whole number.) lower limit A.D. upper limit A.D.TABLE 4 Critical Values for Student's t Distribution one-tail area 0.250 0.125 0.100 0.075 0.050 0.025 0.010 0.005 0.0005 two-tail area 0.500 0.250 0.200 0.150 0.100 0.050 0.020 0.010 010010 0.500 0.750 0.800 0.850 0900 0.950 0.980 0.990 0999 1.000 2.414 3.078 4.165 6.314 12 706 31.821 63.657 636.619 0.816 1.604 1.896 2.282 2.920 4.303 6.965 9.925 31.599 0.765 1.423 1.638 1.924 2.353 3.182 4.541 5.841 12.924 0.741 1.344 1.533 1.778 2.132 2.776 3.747 4.604 8.610 0.727 1.301 1.476 1.699 2.015 2.571 3.365 4.032 6.869 0.718 1.273 1.440 1.650 1.943 2.447 3.143 3.707 5.959 0.711 1.254 1.415 1.617 1.895 2.365 2.998 3.499 5.408 0.706 1.240 1.397 1.592 1.860 2.306 2.896 3.355 5.041 0.703 1.230 1.383 1.574 1.833 2.262 2.821 3.250 4.781 10 0.700 1.221 1.372 1.559 1.812 2.228 2.764 3.169 4.587 11 0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106 4.437 1.2 0.695 1.209 1.356 1.538 1.782 2.179 2.681 3.095 4.318 13 0.694 1.204 1.350 1.530 1771 2.160 2.650 3.012 4.221 14 0.692 1.200 1.345 1.523 1761 2.145 2.624 2.977 4.140 15 0.691 1.197 1.341 1517 1753 2.131 2.602 2.947 4.073 16 0.690 1.194 1337 1.512 1.746 1 2.120 2.583 2.921 4.015 17 0.689 1.191 1.333 1.508 1.740 2.110 2.567 2.898 3.965 18 0.608 1.189 1.330 1.504 1.734 2.101 2.552 2.878 3.922 19 0.698 1.187 1.328 1.500 1.729 2.093 2.539 2.861 3.083 20 0.687 1.185 1.325 1.497 1725 2.086 2.528 2.945 3.850 21 0.686 1.183 1 323 1494 1.721 2.080 2.518 2.831 3.819 22 0.686 1.182 1.321 1.492 1.717 2.074 2.508 2.819 3.792 0.685 1.180 1.319 1.489 1.714 2.069 2.500 2.807 3.768 24 0.685 1.179 1318 1.487 1.711 2.064 2.492 2.797 3.745 25 0.684 1.178 1.316 1.485 1.708 2.060 2.485 2.787 3.725 26 0.684 1.177 1.315 1.483 1.706 2.056 2.479 2.779 3.707 27 0.684 1.176 1.314 1.482 1.703 2.052 2.473 2.771 3.690 0.683 1.175 1.313 1.480 1.701 2.048 2.467 2.763 3.674 29 0.683 1.174 1.311 1.479 1.699 2.045 2.462 2.756 3.059 30 0.603 1.173 1.310 1.477 1.697 2.042 2.457 2.750 3.646 35 0.642 1.170 1.306 1.472 1.690 2.030 2438 2.724 3.591 40 0.681 1.167 1303 1.468 1.694 2.021 2423 2.704 3.951 45 0.680 1.165 1.301 1.465 1.679 2.014 2.412 2.690 3.520 0.479 1.164 1 299 1.462 1.676 3 2.009 2403 2.678 3.496 0.679 1.162 1296 1.458 1.671 2.000 2.390 2.660 3.460 1.294 1.450 1.984 2164025 0.684 1.178 1316 1.485 1708 2.060 2485 2.787 3.725 26 0.684 1.177 1.315 1.483 1.706 2.056 2.479 2.779 3.707 27 0.684 1.176 1.314 1.482 1.703 2.052 2.473 2.771 3.690 28 1.175 1313 1.480 1.701 2.048 2.467 2.763 3.674 29 0.683 1.174 1.311 1.479 1.699 2.045 2.462 2.756 3.059 30 0.683 1.173 1.310 1.417 1.697 2.042 2.457 2.750 3.646 35 0.602 1.170 1.306 1.472 1.690 2.030 2 438 2.724 3.591 40 0.681 1.167 1303 1.468 1.684 2.021 2423 2.704 3.951 45 0.680 1.165 1301 1.465 1.679 2.014 2.412 2.690 3.520 50 0.679 1.164 1.299 1.462 1.676 2.009 2403 2.678 3.496 0.679 1.162 1.296 1.458 1.671 2.000 2.390 2.660 3.460 70 0.678 1.160 1.294 1.456 1.867 1994 2.381 2.648 3.435 0.678 1.159 1.292 1.453 1.064 1.990 2.374 2.639 3.416 100 0.637 1.157 1.290 1.451 1.660 1.984 2.364 2.626 3.390 500 0.675 1.152 1.283 1.442 1.648 1.965 2.334 2.506 3.310 1000 0.675 1.151 1.282 1441 1.646 1.962 2.330 2.501 3.300 0.674 1.150 1.202 1.440 1.645 1.960 2.326 2.576 3.291 For degrees of freedom did not in the table, use the closest all that is smaller