5. A company claims that \(35 \%\) of its peas germinate. In order to test this claim Ann decides to plant 15 of these peas and record the number which germinate.
- State suitable hypotheses for a two-tailed test of this claim.
- Using a \(5 \%\) level of significance, find an appropriate critical region for this test. The probability in each of the tails should be as close to \(2.5 \%\) as possible.
- Ann found that 8 of the 15 peas germinated. State whether or not the company's claim is supported. Give a reason for your answer.
- State the actual significance level of this test.