- Past information shows that \(25 \%\) of adults in a large population have a particular allergy.
Rylan believes that the proportion that has the allergy differs from 25\%
He takes a random sample of 50 adults from the population.
Rylan carries out a test of the null hypothesis \(\mathrm { H } _ { 0 } : p = 0.25\) using a \(5 \%\) level of significance.
- Write down the alternative hypothesis for Rylan's test.
- Find the critical region for this test.
You should state the probability associated with each tail, which should be as close to \(2.5 \%\) as possible.
- State the actual probability of incorrectly rejecting \(\mathrm { H } _ { 0 }\) for this test.
Rylan finds that 10 of the adults in his sample have the allergy.
- State the conclusion of Rylan's hypothesis test.