7. (a) Explain briefly what you understand by
- a critical region of a test statistic,
- the level of significance of a hypothesis test.
(b) An estate agent has been selling houses at a rate of 8 per month. She believes that the rate of sales will decrease in the next month. - Using a \(5 \%\) level of significance, find the critical region for a one tailed test of the hypothesis that the rate of sales will decrease from 8 per month.
- Write down the actual significance level of the test in part (b)(i).
The estate agent is surprised to find that she actually sold 13 houses in the next month. She now claims that this is evidence of an increase in the rate of sales per month.
(c) Test the estate agent's claim at the \(5 \%\) level of significance. State your hypotheses clearly.