Given that \(q < 2 p\), determine the values of \(p\) and \(q\).
The spinner is spun 10 times. Calculate the probability that exactly one 5 is obtained.
Elaine's teacher believes that the probability that the spinner shows a 1 is greater than 0.2 . The spinner is spun 100 times and gives a score of 1 on 28 occasions.
Conduct a hypothesis test at the \(5 \%\) level to determine whether there is any evidence to suggest that the probability of obtaining a score of 1 is greater than 0.2 .