F8 QANT 201 Statistical Sampling Theo ry Question 13) The following table show t

Question

F8 QANT 201 Statistical Sampling Theo ry Question 13) The following table show the standardized math exam scores for a randorm sample of students for three states. The sample included an equal number of eighil fourth-graders. and Tennessee Florida Arizona Grade 260 292 260 287 280 275 260 286 274 247 277 253 290 269 284 297 Fourth Grade 275 248 270 290 295 278 258 287 283 280 270 283 290 2 1 236 240 Perform two-way ANOVA (with replication) using a = 0.05 by defining Factor A as the state and Factor B as to whether the student was an eighth-grader or a fourth-grader. 1. 2. Test the effects that the state and the grade of the student have on the standardized 3. State sources of variation within sample and fill in the table math score P. value crit df MS

Explanation / Answer

applying 2 way ANOVA with replication on above:

from above only Factor A is significant as p value is greater then 0.02.

SUMMARY Tenessee Florida Arizona Total Eighth grade Count 6 6 6 18 Sum 1552 1654 1700 4906 Average 258.6667 275.6667 283.3333 272.5556 Variance 104.2667 181.0667 106.2667 227.6732 fourth grade Count 6 6 6 18 Sum 1470 1676 1694 4840 Average 245 279.3333 282.3333 268.8889 Variance 323.2 63.06667 173.0667 468.2222 Total Count 12 12 12 Sum 3022 3330 3394 Average 251.8333 277.5 282.8333 Variance 245.2424 114.6364 127.2424 ANOVA Source of Variation SS df MS F P-value F crit Factor B 121 1 121 0.76346 0.389189 6.038134 Factor A 6592.889 2 3296.444 20.79921 2.15E-06 4.469551 Interaction 482.6667 2 241.3333 1.522715 0.234503 4.469551 Error 4754.667 30 158.4889 Total 11951.22 35

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