4   Question 1 continued Khalid, a junior researcher, instead suggested evaluating the methods by comparing mean percentage error using a t-test. (b) Make two comments on the suitability of this suggestion. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Lauren, the chief engineer, suggests that, to make the comparison, it would have been better to run both the computer and mathematical models using the same cables, and then testing each to destruction. (c) State, with justification, whether or not you agree with Lauren’s suggestion. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (d) Suggest a test that Lauren could use to compare the two methods. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 1 is 15 marks) Turn over 5   2 A large-scale study of the sleeping habits of students in India was carried out. Students in the study were required to fill out questionnaires about their sleeping habits, which were then used to give a score on a standard Pittsburgh Sleep Quality Index (PSQI). A student with a PSQI score more than a given value was classified as a ‘poor sleeper’. Amongst the study’s reported findings were • the PSQI scores for students had mean 6.45 and standard deviation 2.85 • 20% of students slept for less than 5 hours a night, • 62.6% of students were classified as ‘poor sleepers’. [Source: ncbi.nlm.nih.gov/pmc/articles/PMC4659578] Hamish, a university researcher, is conducting a study to compare the sleeping habits of students in India with those in the UK. He suspects that the proportion of students who sleep for less than 5 hours a night is smaller in the UK than in India. To investigate this, Hamish asks 40 students at his university how many hours they slept the previous night. He finds that 6 of them reported sleeping for less than 5 hours. (a) Making any necessary assumptions, use an exact test to decide whether this sample provides evidence to support Hamish’s suspicion. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________