Question

The State of Arkansas information technology director is considering a new sole source contract for the state’s microcomputer purchases. One factor is reliability. As a test, the director samples 62 state government computers across the three bidding companies and notes whether the computer broke before the warranty expired

                                             Required Repair Before Warranty Expired?

Microcomputer                                  Yes          No

SunPro                                              8            10

ICM                                                   7             21                                                                               

Dellix                                                 8             8

   Select and justify the best test(s). The chi-square, Phi, Yates (or even a combination) might be best for a problem given the data and research question. Do not assume the independent is always on the row.
   Provide the null and alternative hypotheses in formal and plain language for the appropriate test at the 0.05 significance level.
   Do the math and reject/retain null at a=.05. State your critical value.
   Explain the results in plain language.

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 8 10 18 row 2 7 21 28 row 3 8 8 16 TOTALS 23 39 N = 62 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N row 3 row3*col1/N row3*col2/N ------------------------------------------------------------------ expected frequencies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 6.677 11.323 row 2 10.387 17.613 row 3 5.935 10.065 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 8 6.677 1.323 1.75 0.262 10 11.323 -1.323 1.75 0.155 7 10.387 -3.387 11.472 1.104 21 17.613 3.387 11.472 0.651 8 5.935 2.065 4.264 0.718 8 10.065 -2.065 4.264 0.424 ᴪ^2 o = 3.314 ------------------------------------------------------------------ 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 =5.991 since our test is right tailed,reject Ho when ᴪ^2 o > 5.991 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 3.314 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 2 - 1 ) = 2 * 1 = 2 is 5.991 we got | ᴪ^2| =3.314 & | ᴪ^2 α | =5.991 make decision hence value of | ᴪ^2 o | < | ᴪ^2 α | and here we do not reject Ho ᴪ^2 p_value =0.191 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: 3.314 critical value: 5.991 p-value:0.191 decision: do not reject Ho

we do not have enough evidence to support the claim that   the director samples 62 state government computers across the three bidding companies and notes whether the computer broke before the warranty expired.