Question

A high 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 Fail 57 35 61 Hypotheses: Pass/fail rates are dependent on/independent of school. Pass/fail rates are independent of/dependent on school. Enter the expected matrix - round to 4 decimal places. School A School B School C Pass Fail After running an independence test, can it be concluded that pass/fail rates are dependent on school? Yes/No

Answer 1

The pass numbers are independent of the school of study.

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

H₀ : Pass independent of school

Hₐ : Pass independent on school

Two tailed chi square test for independence)

Contingency table is shows as below

School A B C Total

Pass 42 29 45 116

Expected 38.6667 38.6667 38.6667 116.0000667

Obs-exp)^2/observed 0.2874 2.4167 1.0373 3.74138208

df 2    

p value = 0.154

Since p > alpha(0.1) we accept null hypothesis

The pass numbers are independent of the school of study.

Hence we get the required answer.

Learn more about Chi test here:

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