5 At your internship, part of your duties involve determining the quality of par

Question

5 At your internship, part of your duties involve determining the quality of parts received. The following table shows how many of 441 parts you determined to be "perfect·"usable"; or, "unaeceptable." (Totals are shown in the far right column and the bottom row.) Your supervisor asks you some questions about what you have found. Number of Parts Received that are Rejected as Imperfect Unacceptable" but "Usable" "Perfect Vendor A Vendor B Vendor C Vendor D 18 13 25 65 83 103 86 337 140 12 100 a. Your supervisor asks which vendor has the highest proportion of "perfeet" what do you tell her? b. Who supplies the lowest proportion of "unacceptable" parts? What do you say She asks if you believe that there is a relationship between the vendor and the quality of the parts they supply. You say, "I remember from CE319 th at you can use the x' test to see if there is a relationship. It's based on comparing observed and expected values." Chi-squared test for Indendence (Assoclation) Type of test c. What are the null and alternative hypotheses? HO (nul1 hypothesis) H1 (alternative hypothesis) d. What is the critical value of the test statistie? How many degrees of freedom are there? Level of Significance Degrees of freedom Critical value of test statistic e. What value do you obtain for the test statistic and what decision do you make? 596 Abs. value of test statistic Decision(1.e.,accept/reject HO) BLEM #

Explanation / Answer

a. Vendor D is the highest proportion of "perfect" since P = 86/100 = 0.86
b) Vendor D is the lowest proportion of "Unacceptable" since P = 5/111 = 0.045045
c) H0: There is no relationship between the vendor and the quality of the parts they supply
H1:There is relationship between the vendor and the quality of the parts they supply
d) LOS = 5%
degrees of freedom = 6

Critical X^2: 12.59157 at 5% los and 6 df

e) The expected frequencies are

The chisquare contribution values are

Test Statistic, X^2: 8.9909

Here Chisquare value < Chisquare critical value, so we do not reject H0 i.e. we accept H0

thus we conclude that there is no relationship between the vendor and the quality of the parts they supply

Response Unacceptable Unale Perfect Total Vendor A 6.265 13.364 70.371 90 Vendor B 7.0302 14.9977 78.9722 101.0001 Vendor C 9.745 20.789 109.466 140 Vendor D 6.961 14.849 78.19 100 Total 30.0012 63.9997 336.9992 431.0001

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