A large firm receives shipments of an electronic product from three vendors. The
ID: 3318168 • Letter: A
Question
A large firm receives shipments of an electronic product from three vendors. The product is then 3 classified by quality. The table below analyses a recent production run. a. Carefully define the null and alternative hpotheses of the Chi-sq Test which would be b. Fill in gaps marked,2 and '??? d. Wh 12) appropriate for the data analysis. 13] te the assumptions on which the calculations of part b are based at conclusion can the company make from the data analysis if they decide to use a significance level of 10%? Show all your steps in reaching your conclusion. would their decision change if they used a significance level of 5%? Justify your answer. [3] e, Vendor A Vendor B Vendor C A11 12 13.33 20 17.78 Rejected 8.89 30 65 12 14.44 Not perfect 23 28.89 Perfect 85 60 110 255 56.67113.33 All 120 80 160 360 0.13333 + 0.08889 + 0.27778 + 0.08205 0.00000 0.19608 0.09804 1,333 chi-sq ? 0.04274 p-value 2??Explanation / Answer
a) Null: There is no quality difference between the 3 groups
Alternate: The groups differ in quality
b) " * " = 120-21.67- 13.33 =85
" ** " = 360-255-65 = 40
? = (14.44-12)^2 / 14.44 = 0.4123
?? = (3-1)(3-1) = 4
???= 0.8557 = 85.57% ( at 4 DF and chi score = 1.333)
c) It is based on the assumption that the total number of observations adds up to 360. ie, Row sum = Column sum for expected and observed values.
d) 10% < 85.57% So we cannot reject Null hypothesis
Critical chi score = 7.779 at 10%. This is more than 1.333, So it falls in acceptance region
e) No. A smaller pvalue means higher critical chi score. Means the test score is still within acceptance region
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