a box contains exactly 5 shirts with a colour defect
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(ii) a box contains fewer than 15 shirts with a sewing defect
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(iii) a box contains at least 20 shirts which do not have a fabric defect.
Question 18 continues on the next page
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Tiana wants to investigate the proportion, \(p\), of defective shirts with a fabric defect.
She wishes to test the hypotheses
$$\begin{aligned}
& \mathrm { H } _ { 0 } : p = 0.3
& \mathrm { H } _ { 1 } : p < 0.3
\end{aligned}$$
She takes a random sample of 60 shirts with a defect and finds that \(x\) of them have a fabric defect.
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Using a \(5 \%\) level of significance, find the critical region for \(x\).
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(ii) In her sample she finds 13 shirts with a fabric defect.
Complete the test stating her conclusion in context.