In their paper "Testing the claims of a graphologist," Journal of Personality, Vol. 16 (1947), pp. 192-197, G. R. Pascal and B. Suttell describe an experiment designed to evaluate the ability of a professional graphologist. The graphologist claimed that she could distinguish the handwriting of abnormal from that of normal persons. The experimenters selected 10 persons who had been diagnosed as psychotics by at lea.st 2 psychiatrists. For each of these persons a normal-control person was matched for age, sex, and. education. Handwriting samples from each pair of persons were placed in a separate folder and presented to the graphologist, who was able to identify correctly the sample of the psychotic in 6 of the 10 pairs.
(i) What is the probability that she would have been correct on at least 6 pairs just by chance?
(ii) How many correct judgements would the graphologist need to make so that the probability of her getting at least that many correct by chance is 5 % or less?