The number of absences per week by workers at a factory has the distribution $$\(\operatorname{Po}(2.1)\)$$. Following a change in working conditions, the management wished to test whether the mean number of absences has decreased. They found that, in a randomly chosen 3-week period, there were exactly 2 absences. Carry out the test at the $$\(10 \%\)$$ significance level. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_63 Year：2020 Question No：5(d)
Answer:
\( \mathrm{H}_{0}: \lambda=6.3 \)
\( \mathrm{H}_{1}: \lambda<6.3 \)
\( \mathrm{P}(X \leqslant 2)=\mathrm{e}^{-6.3}\left(1+6.3+\frac{6.3^{2}}{2 !}\right) \)
\( \mathrm{P}(X \leqslant 2)=\mathrm{e}^{-6.3}\left(1+6.3+\frac{6.3^{2}}{2 !}\right) \)
\( =0.0498\quad or\quad 0.0499 \)
'0.0498' < \( 0.1 \)
There is evidence that mean number of absences has decreased.
\( \mathrm{H}_{1}: \lambda<6.3 \)
\( \mathrm{P}(X \leqslant 2)=\mathrm{e}^{-6.3}\left(1+6.3+\frac{6.3^{2}}{2 !}\right) \)
\( \mathrm{P}(X \leqslant 2)=\mathrm{e}^{-6.3}\left(1+6.3+\frac{6.3^{2}}{2 !}\right) \)
\( =0.0498\quad or\quad 0.0499 \)
'0.0498' < \( 0.1 \)
There is evidence that mean number of absences has decreased.
Knowledge points:
6.5.2.1 direct evaluation of probabilities
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download