8 There are two hospitals in a city. Over a period of time, the first hospital recorded an average of 20 births a day.
Over the same period of time, the second hospital recorded an average of 5 births a day. Stuart claims that birth rates in the hospitals have changed over time.
On a randomly chosen day, he records a total of 16 births from the two hospitals.
8

1. Investigate Stuart's claim, using a suitable test at the \(5 \%\) level of significance.
   8
2. For a test of the type carried out in part (a), find the probability of making a Type I error, giving your answer to two significant figures.
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