Question

using 0.01 level of significance use the information given to test whether a person's ability in math is independent of his or her interest in calculus.

Ability in math

	Low	Average	High
Low	63	42	15
Average	58	61	31
High	14	47	29

Interest in calculus - left

Answer 1

Given table data is as below MATRIX col1 col2 col3 TOTALS row 1 63 42 15 120 row 2 58 61 31 150 row 3 14 47 29 90 TOTALS 135 150 75 N = 360 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 col3 row 1 row1*col1/N row1*col2/N row1*col3/N row 2 row2*col1/N row2*col2/N row2*col3/N row 3 row3*col1/N row3*col2/N row3*col3/N ------------------------------------------------------------------ expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 row 1 45 50 25 row 2 56.25 62.5 31.25 row 3 33.75 37.5 18.75 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 63 45 18 324 7.2 42 50 -8 64 1.28 15 25 -10 100 4 58 56.25 1.75 3.063 0.054 61 62.5 -1.5 2.25 0.036 31 31.25 -0.25 0.063 0.002 14 33.75 -19.75 390.063 11.557 47 37.5 9.5 90.25 2.407 29 18.75 10.25 105.063 5.603 ᴪ^2 o = 32.139 ------------------------------------------------------------------ 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, α = 0.01 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =13.277 since our test is right tailed,reject Ho when ᴪ^2 o > 13.277 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 32.139 critical value the value of |ᴪ^2 α| at los 0.01 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 3 - 1 ) = 2 * 2 = 4 is 13.277 we got | ᴪ^2| =32.139 & | ᴪ^2 α | =13.277 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0 ANSWERS --------------- 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: 32.139 critical value: 13.277 p-value:0 decision: reject Ho

we have enough evidence to support the claim that there is a association  information given to test whether a person's ability in math is independent of his or her interest in calculus.