P_SEC Statistics & Econometrics Mock Exam
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P_SEC Statistics & Econometrics
Mock Exam
Please answer all questions.
Question 1 [15 marks]
The time taken, in minutes, for 20 employees to complete a particular task are displayed below. 6.5, 5.8, 4.5, 6.2, 4.8, 7.3, 4.6, 3.9, 4.4, 5.5, 5.2, 6.7, 3.0, 2.4, 5.0, 3.6, 2.9, 4.0, 2.8, 3.6
a) Find the positions and then the values of the median, the lower and the upper quartiles. [12 marks]
b) Draw a box-plot for the above data set. [3 marks]
Question 2 [14 marks]
A long-distance taxi service owns two vehicles. These are of different ages and have different repair records. The probabilities that, on any given day, each vehicle will be available for use are 0.95 and 0.9. Whether one vehicle is available is independent of whether the other vehicle is available.
a) Find the probability distribution for the number of vehicles available for use on a given day. [11 marks]
b) Find the expected value of vehicles available for use on a given day. [3 marks]
Question 3 [16 marks]
A machine is built to fill jars with coffee. The weight of the coffee in the jars is normally distributed with mean 100.5g and standard deviation 0.266g. If a jar of coffee is selected at random:
a) Find the probability that the weight of the coffee in the jar is greater than 100.8g. [5 marks]
b) Find the probability that the weight of the coffee in the jar is between 100.3g and 100.7g. [4 marks]
c) Any jar found to contain less than 100g is rejected. Find the percentage ofjars that are rejected. [3 marks]
d) The company building the machine wishes to reduce the percentage of rejected jars to below 1%. What standard deviation should the company be aiming for if the mean is fixed at 100.5g? [4 marks]
Question 4 [5 marks]
Given the simple regression model Y = F0 + F1X and the regression results that follow, test the null hypothesis that the slope coefficient is zero versus the alternative hypothesis of greater than zero using probability of Type I error equal to 5%, and determine the 95% and 99% confidence intervals. It is assumed that the random sample of size n = 38 with b1 = 5 and sb1 = 2.1.
2023-04-20