Question

Construct a confidence interval for, with the sample statistics for mean cholesterol content of a hamburger from two font food chains and confiance erval construction formula below. Assume the populations are approximately normal with a variances Stats - 71 m., 3.74 mg, 17 Xy - 45 m. 12.02 m. - 14 Confidence interval when variances are not equal at is the smaller of 1 Enter the endpoints of the interval 0 Round to the reared integer as needed)

Answer 1

Solution :

Endpoints of the interval is ;

$23.83< \mu_1-\mu_2<28.17$

Solution, i- Here we have given that Xi = 71 mg, S,= 3.74 mgf n = 17 X = 45 mg S = 2.02 mg &n2 = 14 confidence interval is (81-82) - tc (S² + S2 D2 <4=do < 77-7.)tta $+s VO n2 tca to.os, 25 2.060 So, 95% confident interval is. (71-45) – 2.066 9.86 +4.08 (ty-42 < (T145) +2.060* 19.86 17 + 4.08 14 [ 23.83 (41-42 (28. 17] end points of the interval is; 23.83 < Mi-l2 < 28.17

See the critical value by using t table when two tail = 0.05 and df = 25

t Table cum, prob one-tail two-tails 978 0.50 1.00 0.25 0.50 ta 0.20 0.40 0.15 0.30 0.10 0.20 t95 0.05 0.025 0.10 0.05 0.01 0.02 999 0.005 0.001 0.01 0.002 0.0005 0.001 dt 1 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 80 100 1000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0% 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.678 0.677 0.675 0.674 50% 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 0.848 0.846 0.845 0.842 0.842 60% 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.045 1.043 1.042 1.037 1.036 70% 3.078 6.314 12.71 1.886 2.920 4.303 1.638 2.353 3.182 1.533 2.132 2.776 1.476 2.015 2.571 1.440 1.943 2.447 1.415 1.895 2.365 1.397 1.860 2.306 1.383 1.833 2.262 1.372 1.812 2.228 1.363 1.796 2.201 1.356 1.782 2.179 1.350 1.771 2.160 1.345 1.761 2.145 1.341 1.753 2.131 1.337 1.746 2.120 1.333 1.740 2.110 1.330 1.734 2.101 1.328 1.729 2.093 1.325 1.725 2.086 1.323 1.721 2.080 1.321 1.717 2.074 1.319 1.714 2.069 1.318 1.711 2.064 1.316 1.708 2.060 1.315 1.706 2.056 1.314 1.703 2.052 1.313 1.701 2.048 1.311 1.699 2.045 1.310 1.697 2.042 1.303 1.684 2.021 1.296 1.671 2.000 1.292 1.664 1.990 1.290 1.660 1.984 1.282 1.646 1.962 1.282 1.645 1.960 80% 90% 95% Confidence Level 31.82 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.374 2.364 2.330 2.326 98% 63.66 318.31 9.925 22.327 5.841 10.215 4.604 7.173 4.032 5.893 3.707 5.208 3.499 4.785 3.355 4.501 3.250 4.297 3.169 4.144 3.106 4.025 3.055 3.930 3.012 3.852 2.977 3.787 2.947 3.733 2.921 3.686 2.898 3.646 2.878 3.610 2.861 3.579 2.845 3.552 2.831 3.527 2.819 3.505 2.807 3.485 2.797 3.467 2.787 3.450 2.779 3.435 2.771 3.421 2.763 3.408 2.756 3.396 2.750 3.385 2.704 3.307 2.660 3.232 2.639 3.195 2.626 3.174 2.581 3.098 2.576 3.090 99% 99.8% 636.62 31.599 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.690 3.674 3.659 3.646 3.551 3.460 3.416 3.390 3.300 3.291 99.9% z