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 α = 0.05.
Day of Week | M | Tu | W | Th | F |
Nondefective | 87 | 86 | 94 | 87 | 86 |
Defective | 7 | 7 | 13 | 4 | 10 |
(a) Find the test statistic. (Give your answer correct to two
decimal places.)
(ii) Find the p-value. (Give your answer bounds
exactly.)
< p <
applying chi square test:
Observed | Oi | M | Tu | W | TH | F | Total |
non-defective | 87 | 86 | 94 | 87 | 86 | 440 | |
defective | 7 | 7 | 13 | 4 | 10 | 41 | |
total | 94 | 93 | 107 | 91 | 96 | 481 | |
Expected | Ei=row total*column total/grand total | M | Tu | W | TH | F | Total |
non-defective | 85.99 | 85.07 | 97.88 | 83.24 | 87.82 | 440 | |
defective | 8.01 | 7.93 | 9.12 | 7.76 | 8.18 | 41 | |
total | 94 | 93 | 107 | 91 | 96 | 481 | |
chi square χ2 | =(Oi-Ei)2/Ei | M | Tu | W | TH | F | Total |
non-defective | 0.0119 | 0.0101 | 0.1538 | 0.1695 | 0.0376 | 0.383 | |
defective | 0.1279 | 0.1085 | 1.6501 | 1.8195 | 0.4035 | 4.109 | |
total | 0.140 | 0.119 | 1.804 | 1.989 | 0.441 | 4.492 |
a) test statistic =4.49
ii)
p value =0.343
bounds : 0.3 <p value <0.4
The manager of an assembly process wants to determine whether or not the number of defective...
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 α = 0.05. Day of Week M Tu W Th F Nondefective 92...
Question (9) 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 α = 0.05. Day of Week M Tu W Th F Nondefective 85 87 93 86...
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