The manager of an assembly process wants to determine whether or not the number
ID: 3150937 • Letter: T
Question
The manager of an assembly process wants to determine whether or not the number of defective articles manufactured depends on the day of the week the articles are produced. She collected the following information. Is there sufficient evidence to reject the hypothesis that the number of defective articles is independent of the day of the week on which they are produced? Use = 0.05.
(a) Find the test statistic. (Give your answer correct to two decimal places.)
(ii) Find the p-value. (Give your answer bounds exactly.)
_________ < p < ______
Explanation / Answer
Difference Scores Calculations
Treatment 1
N1: 5
df1 = N - 1 = 5 - 1 = 4
M1: 92.4
SS1: 27.2
s21 = SS1(N - 1) = 27.2(5-1) = 6.8
Treatment 2
N2: 5
df2 = N - 1 = 5 - 1 = 4
M2: 10.6
SS2: 93.2
s22 = SS2(N - 1) = 93.2(5-1) = 23.3
T-value Calculation
s2p = ((df1(df1 + df2)) * s21) + ((df2(df2+ df2)) * s22) = ((48) * 6.8) + ((48) * 23.3) = 15.05
s2M1 = s2pN1 = 15.055 = 3.01
s2M2 = s2pN2 = 15.055 = 3.01
t = (M1 - M2)(s2M1 + s2M2) = 81.86.02 = 33.34
The t-value is 33.33919. The p-value is < .00001. The result is significant at p < .05.
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