Given Below is the House prices of 4 different locations A, B, C, and D. Locatio
ID: 3062737 • Letter: G
Question
Given Below is the House prices of 4 different locations A, B, C, and D.
Location A
Location B
Location D
Location C
291500
326700
684000
178000
269000
334700
684000
210000
293200
304700
732000
210000
270700
312700
782000
210000
278700
331200
782000
210000
297200
308700
830000
210000
274700
389200
880000
210000
282700
366700
880000
233000
301200
374700
928000
233000
199000
344700
978000
233000
The F-Statistic and the F-Critical at 1% Type I error are ……, Respectively
4.38 & 248.85, respectively
248.85 & 2.87, respectively
218.85 & 4.28, respectively
None of the above
Location A
Location B
Location D
Location C
291500
326700
684000
178000
269000
334700
684000
210000
293200
304700
732000
210000
270700
312700
782000
210000
278700
331200
782000
210000
297200
308700
830000
210000
274700
389200
880000
210000
282700
366700
880000
233000
301200
374700
928000
233000
199000
344700
978000
233000
Explanation / Answer
Let Ti be the total value for Location i, ni be number of observations of location i.
Let G be the total test scores of all observations and N be total number of observations.
X2 for each location and the entire data set
T1 = 2757900, T2 = 3394000 , T3 = 8160000, T4 = 2137000
G = 2757900 + 3394000 + 8160000 + 2137000 = 16448900
X2 = 768281330000 + 1159533200000 + 6749952000000 + 459151000000 = 9136917530000
SST = X2 - G2/N = 9136917530000 - 164489002/40 = 2372759749750
SSTR = T2/n - G2/N = (27579002 /10 + 33940002 /10 + 81600002 /10 + 21370002 /10 ) - 164489002/40 = 2263603960750
SSE = SSTR - SSE = 2372759749750 - 2263603960750 = 109155789000
DF for SSTR = Number of locations - 1 = 4 - 1 = 3
DF for SSE = N - Number of locations = 40 - 4 = 36
MSTR = SSTR / DF for SSTR = 2263603960750 / 3 = 754534653583
MSE = SSE / DF for SSE = 109155789000 / 36 = 3032105250
F = MSTR / MSE = 754534653583 / 3032105250 = 248.85
DF for F test = DF for SSTR, DF for SSE = 3, 36
Critical value of F for 1% Type I error and DF = 3, 36 is 4.38
So, the answers are 248.85 & 4.38, respectively
So, None of the above is the correct option.
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