Is achieving a basic skill level related to the location of the school? The resu

Question

Is achieving a basic skill level related to the location of the school? The results of a random sample of students by the location of school and the number of students achieving basic skill levels in three subjects is shown in the contingency table. At alpha equals =0.05, test the hypothesis that the variables are independent. Complete parts (a) through (d). Subject Location Reading Math Science Urban 43 47 131 SuburbanSuburban 65 70 67 (a) Identify the claim and state the null and alternative hypotheses. Upper H0: Skill level in a subject is location. Upper H Subscript aHa: Skill level in a subject is dependent on independent of location. The alternative hypothesis null hypothesis is the claim. (b) Determine the degrees of freedom, find the critical value, and identify the rejection region. What are the degrees of freedom? d.f.equals= 4 Find the critical value. chi Subscript 0 Superscript 220equals= nothing (Round to three decimal places as needed.)

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as

null, Ho: no relation b/w X and Y OR X and Y are independent

alternative, H1: exists a relation b/w X and Y OR X and Y are dependent

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =5.991

since our test is right tailed,reject Ho when ^2 o > 5.991

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 28.895

critical value

the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 5.991

we got | ^2| =28.895 & | ^2 | =5.991

make decision

hence value of | ^2 o | > | ^2 | and here we reject Ho

^2 p_value =0

ANSWERS

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null, Ho: no relation b/w X and Y OR X and Y are independent

alternative, H1: exists a relation b/w X and Y OR X and Y are dependent

test statistic: 28.895

critical value: 5.991

p-value:0

decision: reject Ho

MATRIX col1 col2 col3 TOTALS row 1 43 47 131 221 row 2 65 70 67 202 TOTALS 108 117 198 N = 423

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