1. A psychologist is investigating the numbers people choose when asked to pick a number at random in a given interval. He finds that when asked to pick a number between 0 and 100 people are less likely to pick certain numbers, such as multiples of ten. He believes, however that if people are asked to pick an odd number between 0 and 100 they are equally likely to pick a number ending in any of the digits \(1,3,5,7\) or 9 .

To test this theory he asks 80 people to pick an odd number between 0 and 100 and records the last digit of the numbers chosen. His results are shown in the table below. Stating your hypotheses clearly and using a 10\% level of significance test the psychologist’s theory.
(9 marks)