Question

Chronic Remitted X2 = 20.4 Preliminary analyses indicate that you can consider the assumptions for using nonpooled t-procedures satisfied. Researchers randomly and independently selected 33 prisoners diagnosed with chronic posttraumatic stress disorder (PTSD) and 23 prisoners that were diagnosed with PTSD but had since recovered (remitted) x = 29.1 S = 5 S2 = 8 n = 33 = 23 n2 Obtain a 95% confidence interval for the difference, H1 - H2, between the mean ages at arrest for prisoners with chronic PTSD and remitted PTSD. The 95% confidence interval is from 5.518 to 11.882 (Round to three decimal places as needed.)

Answer 1

Chronic a = 29.1 si = 5 ni = 33 Remitted z = 20.4 S₂ 8 n₂ 23 The 95% confidence interval for Hi-t is (52 - 22) - to sit sa (M = H₂ {(2, 2+ to 25

S2 + 5 152 212 8 + 5,4 54 84 t The degrees of freedom on t is: V no 33 23 + SA nen,-1) n (ng-1) 33²x32 232X22 v = 34 degrees of freedom. so, tzu at 2.5% = 2.032 Therefore: Confidence interval is : (29.1 -20,41 -2.032 5²82 <H-Hz<(29.-20.48+ 33 23 2.032 IV 33 23 8.7 4.365 LH, H₂ L 8.7+4.365 4.335 L M - M₂ 2 13.065 5?

Percentage Points for the t distribution This table gives percentage points x defined by the equation 00 dt P= 1 1(12v+2) TvT (12v) X (1+2+/)%*) Р 0 х The limiting distribution of t as v tends to infinity is the standard normal distribution. When v is large, interpolation in v should be harmonic. P= 40% 30% 25% 20% 15% 10% 5% 2.5% 1% 0.5% 0.1% 0.05% V 1 0.3249 0.7265 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66 318.3 636.6 2 0.2887 0.6172 0.8165 1.061 1.386 1.886 2.920 4.303 6.965 9.925 22.33 31.60 3 0.2767 0.5844 0.7649 0.9785 1.250 1.638 2.353 3.182 4.541 5.841 10.21 12.92 4 0.2707 0.5686 0.7407 0.9410 1.190 1.533 2.132 2.776 3.747 4.604 7.173 8.610 5 0.2672 0.5594 0.7267 0.9195 1.156 1.476 2.015 2.571 3.365 4.032 5.894 6.869 6 0.2648 0.5534 0.7176 0.9057 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959 7 0.2632 0.5491 0.7111 0.8960 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408 8 0.2619 0.5459 0.7064 0.8889 1.108 1.397 1.860 - 2.306 - 2.896 3.355 4.501 5.041 9 0.2610 0.5435 0.7027 0.8834 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781 10 0.2602 0.5415 0.6998 0.8791 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587 11 0.2596 0.5399 0.6974 0.8755 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437 12 0.2590 0.5386 0.6955 0.8726 1.083 1.356 1.782 2.179 2.681 3.055 3.930 4.318 13 0.2586 0.5375 0.6938 0.8702 1.079 1.350 1.771 2.160 2.650 3.0123.852 4.221 14 0.2582 0.5366 0.6924 0.8681 1.076 1.345 1.761 2.145 2.624 2.977 3.787 4.140 15 0.2579 0.5357 0.6912 0.8662 1.074 1.341 1.753 2.131 2.602 2.947 3.733 4.073 16 0.2576 0.5356 0.6901 0.8647 1.071 1.337 1.746 2.120 2.583 2.921 3.686 4.015 17 0.2573 0.5344 0.6892 0.8633 1.069 1.333 1.740 2.110 2.567 2.898 3.646 3.965 18 0.2571 0.5338 0.6884 0.8620 1.067 1.330 1.734 2.101 2.552 2.878 3.610 3.922 19 0.2569 0.5333 0.6876 0.8610 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883 20 0.2567 0.5329 0.6870 0.8600 1.064 1.325 1.725 2.086 2.528 2.845 3.552 3.850 21 0.2566 0.5325 0.6864 0.8591 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819 22 0.2564 0.5321 0.6858 0.8583 1.061 1.321 1.717 2.074 2.508 2.819 3.505 3.792 23 0.2563 0.5317 0.6853 0.8575 1.060 1.319 1.714 2.069 2.500 2.807 3.485 3.768 24 0.2562 0.5314 0.6848 0.8569 1.059 1.318 1.711 2.064 2.492 2.797 3.467 3.745 25 0.2561 0.5312 0.6844 0.8562 1.058 1.316 1.708 2.060 2.485 2.787 3.450 3.725 26 0.2560 0.5309 0.6840 0.8557 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707 27 0.2559 0.5306 0.6837 0.8551 1.057 1.314 1.703 2.052 2.473 2.771 3.421 3.689 28 0.2558 0.5304 0.6834 0.8546 1.056 1.313 1.701 2.048 2.467 2.763 3.408 3.674 29 0.2557 0.5302 0.6830 0.8542 1.055 1.311 1.699 2.045 2.462 2.756 3.396 3.660 30 0.2556 0.5300 0.6828 0.8538 1.055 1.310 1.697 2.042 2.457 2.750 3.385 3.646 32 0.2555 0.5297 0.6822 0.8530 1.054 1.309 1.694 2.037 2.449 2.738 3.365 3.622- 34 0.2553 0.5294 0.6818 0.8523 1.052 1.307 1.691 2.032 2.441 2.728 3.348 3.601 36 0.2552 0.5291 0.6814 0.8517 1.052 1.306 1.688 2.028 2.434 2.719 3.333 3.582 38 0.2551 0.5288 0.6810 0.8512 1.051 1.304 1.686 2.024 2.429 2.712 3.319 3.566 40 0.2550 0.5286 0.6807 0.8507 1.050 1.303 1.684 2.021 2.423 2.704 3.307 3.551 50 0.2547 0.5278 0.6794 0.8489 1.047 1.299 1.676 2.009 2.403 2.678 3.261 3.496 60 0.2545 0.5272 0.6786 0.8477 1.045 1.296 1.671 2.000 2.390 2.660 3.232 3.460 120 0.2539 0.5258 0.6765 0.8446 1.041 1.289 1.658 1.980 2.358 2.617 3.160 3.373 0.2533 0.5244 0.6745 0.8416 1.036 1.282 1.645 1.960 2.326 2.576 3.090 3.291