Sample sizes, means, and standard deviations by seating location for female stud

Question

Sample sizes, means, and standard deviations by seating location for female student height and preferred classroom seating are given in the following table.

(a) Find SS Groups. (Round the answer to the nearest whole number.)
SS Groups =  

(b) Use the following formula to find the SS Error, SE. (Round the answer to the nearest whole number.)

SE =  

(c) The value of df for error is 142. Find the value of MSE. (Round the answer to the nearest thousandth.)
MSE =  

Find the value of the pooled standard deviation sp. (Round the answer to the nearest thousandth.)
sp =

Location N Mean Std.Dev. Front 36 63.79 2.07 Middle 85 64.84 2.84 Back 24 66.52 2.74 All 145 64.86 SS Error = E (n - 1); groups

Explanation / Answer

from above:

a)SSG =107.384~ 107

b)SSE =1000

c) MSE =1000/142 =7.042

sp =2.654

( please revert if any answer is wrong as this may happen due to rounding error)

i ni xi S2i ni*(Xi-Xgrand)2 (ni-1)*S2i front 36 63.79 4.285 41.015 149.972 middle 85 64.84 8.066 0.026 677.510 back 24 66.52 7.508 66.343 172.675 Grand mean=Xgrand=xi*ni/ni= 64.86 107.384 1000.157 SSG SSE Source of variation SS df MS F treatment 107.384 2 53.692 7.623 error 1000.157 142 7.043 total 1107.541 144

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