Question

Part D. The average grade of 32 Nano Engineering students in STAT 353 is 75% with a standard deviation of 5%. The average grade of 27 Mech Engineering students in STAT 353 is 78% with a variance of 36%. Students are either in Mech or in Nano. Assuming the standard deviation between the two groups is the same, build a 95% confidence interval to compare the difference in the means of the two groups.

Answer 1

Part o) let SIAT 353 32) The grade of Nano Engineering students in (i=l2.. The grade of Mech engineering students in (i=12 27) 2 STAT 353 we have given that 75 Se=5 ni= 32 n2=27 52=/36 = 6 Now we know that 100 (1-2)% confidence interval for the difference in the means of populations when population vandhce is unknown ( (fy) - thith2-262 s B-T) + ni n2 thith2-2 2/2 V ni na where s2 (n-1) sok + (n2-1) sy? nithz-2 ( 32-1) (5)2 + (27-1) (612 32+27-2 30.0175 il 'S: 5.4788 the two groups Here we have to find 95% interval to compare the difference in the means of so tnitm-2 2/2 = t 32+27- +32+27-20.05 t57 0.025 = 2.00 2 CS Scanned with CamScanner

lower bound for C.I (do- tntn -2 2/2 S ni 12 175-79) - (2.002 x 5.4788 32 27 - 5.8663 1 Upper bound (x-7)+ thitha-2,212 for c. I S ni nz (75-787 + ( 2.002% 5.4788 tett 32 27 11 - O.1337 95% confidence interval for difference in the means of the two groups is (-5.8663-0.1337) CS Scanned with CamScannen

t table as follows:

7:43 62.0 KB/S 774 Edit 26 Х t-distribution Confidence Level 85% 90% 95% 98% 60% 70% 80% 99% 99.8% 99.9% 2 Tailed 1 Tailed 0.40 0.20 0.30 0.15 0.20 0.10 Level of Significance 0.15 0.10 0.05 0.02 0.075 0.05 0.025 0.01 0.01 0.005 0.002 0.001 0.001 0.0005 26.30 12.39 8.499 6.835 5.946 5.403 5.039 0.039 4.780 2.822 3.250 df 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14 15 16 17 18 19 20 21 22 23 24 25 4.586 4.437 1.376 1.963 3.133 4.195 6.320 12.69 31.81 63.67 1.060 1.385 1.883 2.278 2.912 4.271 4.271 6.816 9.520 0.978 1.250 1.637 1.924 2.352 3.179 4.525 5.797 0.941 1.190 1.533 1.778 2.132 2.776 3.744 4.596 0.919 1.156 1.476 1.699 2.015 2.570 3.365 4.030 0.906 1.134 1.440 1.650 1.943 2.447 3.143 3.707 0.896 1.119 1.415 1.617 1.895 2.365 2.999 3.500 0.889 1.108 0.00% 1.397 1.592 1.860 2.306 2.897 3.356 0.000 0.883 1.100 1.383 1.574 1.833 2.262 0.879 1.372 1.093 V. 1.559 1.813 2.228 2.764 3.170 0.875 0.00 1.088 1.363 1.305 1.548 1.796 2.201 2.719 3.106 0.873 1.083 1.356 1.538 1.782 2.179 2.682 3.055 0.870 1.079 1.350 1.530 1.771 2.160 2.651 3.013 0 000 0.868 1.076 1.345 1.523 1.761 . 15 2.145 2.625 2.977 0.866 1.074 1.341 1.517 1.753 2.131 2.603 2.947 0.865 1.071 1.337 1.512 1.746 2.120 2.584 2.921 0.863 1.069 1.333 1.508 1.740 2.110 2.567 2.899 0.862 1.067 1.330 1.504 1.734 2.101 2.553 2.879 0.861 1.000 1.066 1.328 1.500 1.000 1.729 2.095 2.093 2.540 2.861 0.860 1.064 1.325 1.497 19 1.725 .125 2.086 2.529 2.840 0.859 1.063 1.323 1.494 1.721 2.080 2.518 2.832 0.858 1.061 1.321 1.717 2.074 2.074 2.509 2.819 0.857 1.060 1.319 1.489 1.714 2.069 2.500 2.808 0.857 1.487 1.711 2.064 2.493 2.797 0.856 1.058 1.485 1.708 2.060 2.486 2.788 0.856 1.058 1.315 1492 1.483 1.706 2.056 2.479 2.779 0.855 1.057 1.314 ora 1.482 1.703 2.052 2.473 more 2.473 2.771 1994 0.855 1.056 1.313 1.480 1.701 2.048 2.468 2.764 MORALES 1120 1.055 Icon 0.854 1.311 1.479 1.699 2.045 2.463 2.757 LE 0.854 1.055 1.310 2019 20 1.477 1.697 Movie 2.042 2.458 2.750 0.851 1.050 1.303 Tied 10 201 202 203 1.468 1.684 2.021 2.424 2.705 dou 0 0 100 0.849 1.047 1.299 1.462 1.676 2.009 2.404 2.678 0.848 0 1 1.045 1.296 1.458 1.671 2.000 2.391 2.661 0.847 1.044 1.294 1.456 1.667 1.994 2.381 2.648 0.846 1.043 1.292 1.453 1.664 1.990 2.374 2.639 0.846 1.042 1.291 1.452 1.662 1.987 2.369 2.632 0.845 1.042 1.290 1.451 1.660 1.984 2.365 2.626 19.65 9.937 7.115 5.876 5.201 4.783 4.500 4.297 4.297 4.144 4.025 3.930 3.930 3.852 3.788 3.733 3.687 3.646 3.611 3.580 4.318 4.221 4.141 4.073 4.015 3.965 3.922 3.884 3.850 3.552 3.820 1.492 1.059 1.318 1.316 27 28 29 30 40 50 60 70 80 90 100 3.528 3.505 3.485 3.467 3.451 3.435 3.421 3.409 3.397 3.386 3.307 3.262 3.232 3.211 3.196 3.184 3.174 3.792 3.768 3.746 3.725 2707 3.707 con 3.690 3.674 3.660 3.646 3.551 3.496 3.460 10 3.435 3.417 3.402 3.391 0842 1.036 1.282 1.440 1.645 1.960 2.327 2.576 3.091 3.291 סס w DD Tools Mobile View Share PDF to DOC