# Hypothesis testing

#1
Linda regularly takes a taxi to work five times a week. Over a long period of time she finds the taxi is late once a week on average. The taxi firm changes her driver and Linda thinks the taxi is late more often. In the first week with the new driver the taxi is late 3 times.
You may assume that the number of times the taxi is late in a week can be modelled with a binomial distribution.
a Test, at the 5% level of significance, whether or not there is evidence of an increase in the proportion of times the taxi is late. State your hypotheses clearly. (6 marks)
b One of the assumptions when modelling using a binomial distribution is that the probability of success p, in this case the probability the taxi is late, is constant throughout all the trials. Give two possible reasons why this assumption may not hold for this situation. (2 marks)

I got this so far:

X~B(5,p)
H0: p =
H1: p>

I don't really know what to do next
0
3 years ago
#2
For a binomial distribution, E(X) = np. You are given E(X) and n in the question so are well placed to find the p you need for you hypotheses.
0
X

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