HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 312
Inference testing using the Chi2 test
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Inference testing using the Chi2 test A teacher wishes to decide, at the 5% level of significance, whether the performance in a problem solving test is independent of the students' year at school. The teacher selected 120 students, 40 from each of Years 8, 9 & 10, and graded their performance in a test as either A or B. Year 8 9 10 Total Grade awarded A B 22 18 26 14 27 13 75 45 Total 40 40 40 120 The table above right shows the results of his testing. The hypotheses being tested are: H0: There is no relationship between grades awarded and years at school. They are independent. HA: There is a relationship. If H0 is true then the expected frequencies should be those in the table on the right. Year 8 9 10 Total Grade awarded A B 25 15 25 15 25 15 75 45 Total 40 40 40 120 Enter the observed and expected frequencies into columns C1 and C2 of the Statistics aplet. In the HOME view, perform the calculation shown right. This calculates the individual χ 2 values ready for summing as per the formula ∑ χ 2 = (O − E )2 , where O and E are the observed and expected E frequencies. After first changing to the SYMB view to register C3, the required total for C3 can be found in the view. In this case, 1.493. 312
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