Question

Example 4: Four mach 1. A. Four machines A, B, C and D are used to ice a certain kind of cotton fabrics. Samples of size 4 with each unit as 100 square metres are selected from the outputs of the machines at random, and the number of flaws in each 100 square metres are counted, with the following result: A B C D | 11 7 12 16 | 9 9 | 11 20 14 10 18 23 1649 21 Do you think that there is a significant difference in the cs performance of the four machines?

Answer 1

4.

Given table data is as below MATRIX col1 col2 col3 TOTALS TOTALS row 2 11 7 12 16 46 row 3 9 9 11 20 49 row 3 14 10 18 23 65 row 4 16 4 9 21 50 TOTALS 50 30 50 80 210 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 col3 col4 row 2 row1*col1/N row1*col2/N row1*col3/N row1*col4/N row 3 row2*col1/N row2*col2/N row2*col3/N row2*col4/N row 3 row3*col1/N row3*col2/N row3*col3/N row3*col4/N row 4 row4*col1/N row4*col2/N row4*col3/N row4*col4/N ------------------------------------------------------------------ expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 col4 row 2 10.952 6.571 10.952 17.524 row 3 11.667 7 11.667 18.667 row 3 15.476 9.286 15.476 24.762 row 4 11.905 7.143 11.905 19.048 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 11 10.952 0.048 0.002 0 7 6.571 0.429 0.184 0.028 12 10.952 1.048 1.098 0.1 16 17.524 -1.524 2.323 0.133 9 11.667 -2.667 7.113 0.61 9 7 2 4 0.571 11 11.667 -0.667 0.445 0.038 20 18.667 1.333 1.777 0.095 14 15.476 -1.476 2.179 0.141 10 9.286 0.714 0.51 0.055 18 15.476 2.524 6.371 0.412 23 24.762 -1.762 3.105 0.125 16 11.905 4.095 16.769 1.409 4 7.143 -3.143 9.878 1.383 9 11.905 -2.905 8.439 0.709 21 19.048 1.952 3.81 0.2 ᴪ^2 o = 6.009 ------------------------------------------------------------------ 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 = 0.05 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =16.919 since our test is right tailed,reject Ho when ᴪ^2 o > 16.919 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 6.009 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 4 -1 ) * ( 4 - 1 ) = 3 * 3 = 9 is 16.919 we got | ᴪ^2| =6.009 & | ᴪ^2 α | =16.919 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.739 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: 6.009 critical value: 16.919 p-value:0.739 decision: do not reject Ho

we do not have enough evidence to support the claim that significant difference in the performance of the four machines.