8 In a small town, the number of properties sold during a week in spring by a local estate agent, Keith, can be regarded as occurring independently and with constant mean \(\mu\). Data from several years have shown the value of \(\mu\) to be 3.5 .
A new housing development was built on the outskirts of the town and the properties on this development were offered for sale by the builder of the development, not by the local estate agents.
During the first four weeks in spring, when properties on the new development were offered for sale by the builder, Keith sold a total of 8 properties.
Keith claims that the sale of new properties by the builder reduced his mean number of properties sold during a week in spring.
8
- Investigate Keith's claim, using the \(5 \%\) level of significance.
[0pt]
[6 marks]
8 - For your test carried out in part (a) state, in context, the meaning of a Type II error.
[0pt]
[1 mark]
8 - State one advantage and one disadvantage of using a 1\% significance level rather than a 5\% level of significance in a hypothesis test.
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[2 marks]