A mobile phone company claims that each year \(5 \%\) of its customers have their mobile phone stolen. An insurance company claims this percentage is higher. A random sample of 30 of the mobile phone company's customers is taken and 4 of them have had their mobile phone stolen during the last year.
Test the insurance company's claim at the \(10 \%\) level of significance. State your hypotheses clearly.
A new random sample of 90 customers is taken. A test is carried out using these 90 customers, to see if the percentage of customers who have had a mobile phone stolen in the last year is more than 5\%
Using a suitable approximation and a \(10 \%\) level of significance, find the critical region for this test.