7 Company \(A\) uses a machine to produce toys. The number of toys in a week that do not pass Company \(A\) 's quality checks is modelled by a Poisson distribution \(X\) with standard deviation 5 The machine producing the toys breaks down.
After it is repaired, 16 toys in the next week do not pass the quality checks.
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1. Investigate whether the average number of toys that do not pass the quality checks in a week has changed, using the \(5 \%\) level of significance.
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2. For the test carried out in part (a), state in context the meaning of a Type II error. 7
3. Company \(B\) uses a different machine to produce toys.
   The number of toys in a week that do not pass Company B's quality checks is modelled by a Poisson distribution \(Y\) with mean 18 The variables \(X\) and \(Y\) are independent.
   Find the distribution of the total number of toys in a week produced by companies \(A\) and \(B\) that do not pass their quality checks. 7
4. State two reasons why a Poisson distribution may not be a valid model for the number of toys that do not pass the quality checks in a week. Reason 1 \(\_\_\_\_\)
   Reason 2 \(\_\_\_\_\)