6 UKEQ1023 QUANTITATIVE TECHNIQUES II Section B (Continued) Q3. (a) A professor has 2 classes in biology; a morning class of 9 students and an afternoon class of 10 students. On a final examination scheduled at the same time for all students, the classes received the grades shown in the table. Morning Class 73 87 79 75 82 66 95 75 70 Afternoon Class 86 81 84 88 90 85 84 92 83 91 (i) What is the appropriate test to be used if the population is not normally distributed? State the reason for your answer. (3 marks) (ii) Can one conclude at the 0.05 significance level that the morning class performed worse than the afternoon class? (11 marks) (b ) A supermarket sells potatoes in small packs of 1.2kg. A sample of 13 packs was selected at random, and their weights were measured. The mean weight per pack was 1.19kg, and the standard deviation was 0.03kg. Assume that the weight of the packs is normally distributed. (i) Test at the 10% level of significance whether the packs are significantly underweight. (8 marks) (ii) Construct a confidence interval at 95% for the population mean. (Assume if the population standard deviation is 0.015kg). (6 marks) (iii) Interpret your results in Q3. (b) (ii) above if a lower standard deviation is used. (2 marks) [Total: 30 marks]