Question

A researcher has used a one-way analysis of variance model to test whether the average starting salaries differ among recent graduates from the nursing, engineering, business, and education disciplines. She has randomly selected four graduates from each of the four areas. If MSE = 4, and SST= 120, is there a significant difference in the starting salaries among the four disciplines? What are Fstat and Fcrit values?

Select one:

a. No, 6.0, 3.49

b. No, 2.0, 2.49

c. None of the answers

d. Yes, 6.0, 3.49

e. Yes, 2.0, 2.49

Answer 1

Given, MSE = 4 and SST = 120

Let number of groups = k

k = 4 ( as four areas are considered )

Let Total number of items in these groups = n

Here, n = 16 ( as four graduates from each of group are considered )

Fstat = MST / MSE

MST = SST / ( k -1 )

MST = 120 / (4-1) = 120/3 = 40

Therefore, Fstat = 40/4 = 10

Fstat = 10

Fcrit value is observed from F-distribution table. As 'alpha' value is not given let us assume level of significance i.e., alpha at 5%.

F-distribution table at 5% level of significance is shown in the image below:

Appendix 4a 5 per cent Points of the F-distribution Column represents degrees of freedom (v) for numerator of F-test Row represents degrees of freedom (v) for denominator of F-test 1 2 3 4 5 6 7 8 9 10 12 24 0 1 2 3 4 5 6 7 8 9 161.4 18.51 10.13 7.709 6.608 5.987 5.591 5.318 5.117 199.5 215.7 224.6 230.2 19.00 19.16 19.25 19.30 9.552 9.277 9.117 9.013 6.944 6.591 6.388 6.256 5.786 5.409 5.192 5.050 5.143 4.757 4.534 4.387 4.737 4.347 4.120 3.972 4.459 4.066 3.838 3.688 4.256 3.863 3.633 3.482 234.0 236.8 19.33 19.35 8.941 8.887 6.163 6.094 4.950 4.876 4.284 4.207 3.866 3.787 3.581 3.500 3.374 3.293 238.9 240.5 19.37 19.38 8.845 8.812 6.041 5.999 4.818 4.772 4.147 4.099 3.726 3.677 3.438 3.388 3.230 3.179 241.9 19.40 8.785 5.964 4.735 4,060 3.637 3.347 3.137 243.9 19.41 8.745 5.912 4.678 4.000 3.575 3.284 3.073 249.1 19.45 8.638 5.774 4.527 3.841 3.410 3.115 2.900 254.3 19.50 8.526 5.628 4.365 3.669 3.230 2.928 2.707 10 4.965 4.103 3.708 3.478 3.326 3.217 3.135 3.072 3.020 2.978 2.913 2.737 2.538 11 4.844 3.982_3.587_3.357 3.204 3.095 3.012 2.948 2.896 2.854 2.788 2.609 2.405 12 4.747 3.885 3.490 3.259 3.106 2.996 2.913 2.849 2.796 2.753 2.687 2.505 2.296 13 4.667 3.806 324113.179 3.025 2.915 2.832 2.767 2.714 2.671 2.604 2.420 2.206 14 4.600 3.739 3.344 3.112 2.958 2.848 2.764 2.699 2.646 2.602 2.534 2.349 2.131 15 4.543 3.682 3.287 3.056 2.901 2.790 2.707 2.641 2.588 2.544 2.475 2.288 2.066 16 4.494 3.634 3.239 3.007 2.852 2.741 2.657 2.591 2.538 2.494 2.425 2.235 2.010 17 4.451 3.592 3.197 2.965 2.810 2.699 2.614 2.548 2.494 2.450 2.381 2.190 1.960 18 4.414 3.555 3.160 2.928 2.773 2.661 2.577 2.510 2.456 2.412 2.342 2.150 1.917 194.381 3.522 3.127 2.895 2.740 2.628 2.544 2.477 2.423 2.378 2.308 2.114 1.878 20 21 22 23 24 25 26 27 28 29 4.351 3.493 4.325 3.467 4.301 3.443 4.279 3.422 4.260 3.403 4.242 3.385 4.225 3.369 4.210 3.354 4.196 3.340 4.183 3.328 3.098 3.072 3.049 3.028 3.009 2.991 2.975 2.960 2.947 2.934 2.866 2.711 2.599 2.514 2.447 2.393 2.348 2.278 2.082 .843 2.840 2.685 2.573 2.488 2.420 2.366 2.321 2.250 2.054 1.812 2.817 2.661 2.549 2.464 2.397 2.342 2.297 2.226 2.028 1.783 2.796 2.640 2.528 2.442 2.375 2.320 2.275 2.204 2.005 1.757 2.776 2.621 2.508 2.423 2.355 2.300 2.255 2.183 1.984 1733 2.759 2.603 2.490 2.405 2.337 2.282 2.236 2.165 1964 1.711 2.743 2.587 2.474 2.388 2.321 2.265 2.220 2.148 1.946 1.691 2.728 2.572 2.459 2.373 2.305 2.250 2.204 2.132 1.930 1.672 2.714 2.558 2.445 2.359 2.291 2.236 2.1902.118 1.915 1.654 2.701 2.545 2.432 2.346 2.278 2.223 2.177 2.104 1.901 1.638 (continued)

From the above table, we can see on the ( n - k )th i.e., 12th ( 16 - 4 ) column and ( k - 1)rd i.e., 3rd ( 4 - 1 ) row we find that Fcrit value which is 3.49.

Fcrit = 3.49

As Fstat (10 ) is higher than Fcrit ( 3.49 ), Yes, there is significant difference between the starting salaries among the four disciplines.

So, the answer to the question is (c).