Ahigh school offers math placement exams for incoming freshmen to place students into the appropriate math class during their freshman year. three different middle schools were sampled and the following pass/fail results were found. run a test for independence at the 0.10 level of significance. school a school b school c pass 42 29 45

Step-by-step explanation:

Given that a high  school offers math placement exams for incoming freshmen to place students into the appropriate math class during their freshman year

Set up hypotheses as

(Two tailed chi square test for independence)

Contingency table is shows as below

SchoolABCTotal

Pass422945116

Expected38.666738.666738.6667116.0000667

(Obs-exp)^2/observed0.28742.41671.03733.74138208

df2    

p value = 0.154

Since p > alpha(0.1) we accept null hypothesis

The pass numbers are independent of the school of study.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

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