- In the manufacture of cloth in a factory, defects occur randomly in the production process at a rate of 2 per \(5 \mathrm {~m} ^ { 2 }\)
The quality control manager randomly selects 12 pieces of cloth each of area \(15 \mathrm {~m} ^ { 2 }\).
- Find the probability that exactly half of these 12 pieces of cloth will contain at most 7 defects.
The factory introduces a new procedure to manufacture the cloth. After the introduction of this new procedure, the manager takes a random sample of \(25 \mathrm {~m} ^ { 2 }\) of cloth from the next batch produced to test if there has been any change in the rate of defects.
- Write down suitable hypotheses for this test.
- Describe a suitable test statistic that the manager should use.
- Explain what is meant by the critical region for this test.
- Using a 5\% level of significance, find the critical region for this test. You should choose the largest critical region for which the probability in each tail is less than 2.5\%
- Find the actual significance level for this test.