• 

SECTION A: STRUCTURED QUESTIONS (100 MARKS) ANSWER ALL QUESTIONS QUESTION 1 (3|) MARKS) 3. Identify the level of measurement and type of variable for each statement below: i. The average day temperature recorded at 14 cities in Malaysia. (I mark) ii. The time required to produce each tyre on an assembly line. (I mark) iii. The age of each of your employees. (I mark) iv. The ranking of four machines in your plan aer they have been designed as excellent, good, satisfactory or poor. (I mark) 17. Bank 3m Public Service Department wants to carry out a survey on students studying overseas under its sponsorship. The objective of the study is to collect information on the problems faced by them. i. State the most suitable data collection method for this study. (2 marks) ii. Explain why the method you chose is better than the others. (4 marks) c. Consider a data set of air Pollumnt Index for a random sample of area in Southern \"\"ion. '1' 178 116 296 198 157 178 249 178 116 95 148 335 260 : l + l " . i. Calculate median for the data. (3 marks) u. Calculate mean and standard deviation. ( 7 marine) ui. Find the rst quartile and third quartile for these dam. (6 marks) iv. Sketch the shape of air Pollutant Index distn'bution and determine the m. (Hint: use value of median and mean) (4 marks) QUESTION 2 (3|) MARKS) a. A discrete random variable X has the probability function K(1-x)2 x=-I,0,1and'2 P(X=x = 0 otherwise 1. Shows that K =2 (1 marks) ii. Find E[X). (3 marks) 4 mi. Show that [10(1) = E {4 marks) QUESTION 3 (40 MARKS) b. A biased die with six faces is rolled. The discrete random variable X represents the score on the uppermost face. The probability distribution of X is shown in table a. Answer the following questions: below: X 2 3 4 5 6 i. If you use a 0.10 level of significance in a (two-tail) hypothesis test, what is your P(X) a a a b b 0.3 decision rule for rejecting a null hypothesis that the population mean is 400 if you use the Z test? (3 marks) i. Given that E(X) = 4.2, find the value of a and b. (5 marks) If you use a 0.05 level of significance in a (one-tail) hypothesis test, what is your decision on Hi:M