2. A savings and loan association needs information concerning checking balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a sample standard deviation (s) of $297.29 a) Find a 98% confidence interval for the true mean checking account balance for local balances (USE THE t Distribution. b) Find a 95% confidence interval for the variance and standard deviation for this group (USE THE CHI-SQUARE DISTRIBUTION)Critical Values for Student's f Distribution c is a confidence level 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 0.0010 d.f. C 0.500 0.750 0.800 0.850 0.900 0.950 0.980 0.990 0.999 Area c 1.000 2.414 3.078 4.165 6.314 12.706 31.821 63.657 636.619 0.816 1 604 1 886 2.282 2920 4303 6.965 9.925 31.599 -f 0.765 1.423 1.638 1.924 2.353 3.182 4.541 5.841 12.924 4 0.741 1344 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 1943 2.447 3.143 3.707 5.959 0.711 1.254 1.415 1.617 1.895 2365 2.998 3.499 5.408 One-tail area 0.706 1.240 1.397 1.592 1 860 2306 2.896 3.355 5.04 9 0.703 1.230 1383 1.574 1.833 2.262 2821 3.250 4.781 10 0.700 1 1.221 1.372 1.559 1.812 2.228 8 2.764 3.169 4.587 11 0.697 1.214 1363 1.548 1.796 2.201 2.718 3.106 4.437 Right-tail area 12 0.695 1 209 1.356 1.538 1.782 2.179 2.681 3.055 4318 13 0.694 1.204 1.350 1.530 1.771 2.160 2.650 3.012 1.221 14 0692 1200 1345 1.523 1.761 2.145 2.624 2.977 4.140 15 0.691 1.197 1.341 1.517 1.753 2.131 2.602 2.947 4.073 16 0.690 1.194 1.337 1.512 1.746 2.120 2583 2921 4015 17 0.689 1.191 1.333 1.508 1.740 2.110 2.567 2.898 3.965 18 0.688 1.189 1.330 1.504 1.734 2.101 2.552 2.878 3.922 19 0.688 1.187 1.328 1.500 1.729 2.093 2.539 2.861 3.883 Left-tail 20 0.687 1.185 1.325 1.497 1.725 2086 2.528 2.845 3.850 area 21 0.686 1.183 1.323 1.494 1.721 2080 2.518 2831 3.819 22 0.686 1.182 1.321 1.492 1.717 2.074 2.508 2.819 3.792 23 0.685 1.180 1.319 1.489 1.714 2.069 2.500 2.807 3.768 24 0.685 1.179 1.318 1.487 1.711 2064 2.492 2.797 3.745 25 0.684 1.198 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 Two-tail area 28 0.683 1.175 1.313 1.480 1.701 1 2048 2.467 2.763 3.674 29 0.683 1.174 1.311 1.479 1.699 9 2045 2.462 2.756 3.659 30 0.683 1.173 1.310 1.477 1.697 2042 2.457 2.750 3.646 35 0.682 1.170 1306 1.472 1.690 2030 2438 2.724 3.591 40 Area 0.681 1.167 1303 1.468 1 684 2021 2423 2.704 3.551 45 0.680 1.165 1.301 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 2.403 2.678 3.496 60 0.679 1.162 1.296 1.458 1.671 2.000 2390 2.660 3.460 70 0.678 1.160 1.294 1.456 1.667 1.994 2.381 2.648 3.435 80 0.678 1.159 1.292 1.453 1.664 1.990 2.374 2.639 3.416 100 0.677 1.157 1.290 1.451 1 660 1984 2364 2.626 3.390 500 0.675 1.152 1.283 1.442 1.648 1965 2.334 2.586 3.310 1000 0.675 1.151 1.441 1.646 1 1.962 2.330 2.581 3.300 0.674 1.150 1.282 1.440 1.645 1.960 2.326 2.576 3.291