Historically, when spotlighting in a particular reserve ecologists see bandicoots 40% of the time. This year they have been spotlighting 20 times and have seen bandicoots on 3 occasions. They want to test if the probability of seeing bandicoots has reduced, or if this year's results could just be due to chance.

a) [1 mark] What should their null hypothesis be?

b) [1 mark] What should their alternative hypothesis be?

c) [2 marks] What conditions would need to be met for the number of trips to the reserve that result in bandicoot sightings to follow a Binomial distribution?

d) [3 marks] Would it be reasonable to approximate the Binomial distribution with a normal distribution? If so, what values would you use for the mean and standard deviation?

e) [3 marks] Using either the normal approximation or the Binomial distribution directly, calculate a p-value to assess the evidence against the null. Show all your working including any Excel commands you used.

f) [2 marks] Interpret the p-value.