ECON Semester 1 PASS Mock Mid-Semester Exam ANSWERS

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1 ECON Semester 1 PASS Mock Mid-Semester Exam ANSWERS MULTIPLE CHOICE QUESTIONS 1. Unemployment rates are an example of: a. Cross-sectional, quantitative, continuous data b. Time-series, quantitative, continuous data c. Cross-sectional, quantitative, discrete data d. Time-series, quantitative, discrete data e. None of the above 2. Mel & Kochi want to know whether John Howard or Kim Beazley is the preferred PM of Australia. They decide to find the answer by asking people who ring the show. Mel & Kochi s results will be biased due to: a. Measurement error b. Coverage error c. Sampling error d. Non-response error e. Both b & c 3. Jack is at the zoo. He is curious as to the average length of the tusks of elephants. He decides to divide the zoo s elephants into groups by gender and then choses five elephants from each group to calculate the average length of their tusks. Jack is using: a. Cluster sampling b. Simple random sampling c. Stratified sampling d. Systematic sampling e. None of the above. 4. The annual returns of Carlton United over 3 consecutive years have been 12.5%, % and 33.9%. The best estimate of the average annual rate of return over this three year period is a % b % c % d. 8.03%

2 5. Which of the following is NOT a measure of variation? a. Coefficient of variation b. Geometric mean c. Interquartile Range d. Standard Deviation e. All are measures of variation 6. In the 2004 Miss Universe Competition, Jennifer Hawkins scored 73% in humanitarian efforts, 97% in the natural beauty segment and 48% in her talent segment, dancing. Find her average score if the talent segment was worth 10% and the natural beauty segment was worth 75%. a % b % c % d % 7. A certain MBS program has 500 students of whom 150 are married. The probability that exactly 5 of 15 the randomly selected students are married is; a b c d The expected value of a random variable X is 10, and its variance is 30. The expected value for a random variable Y is 20 and its variance is 55. The covariance between X and Y is 11. What is the Var(X+Y)? a. 30 b. 107 c. 55 d Which of the following is FALSE? a. Mutually exclusive variable means that there is no overlap between values. b. Collectively exhaustive means that there is a full sample space, nothing is left out. c. The sum of the probabilities of a collectively exhaustive variable adds to 2 d. Each outcome for a discrete probability distribution is an independent event 2

3 10. If we know that events A & B are mutually exclusive, then P(A and B) = a. 1, because with mutually exclusive events, one must occur and so either A or B will occur with certainty b. 0.5, because each event has an equally likely chance of occurring c. 0, because mutually exclusive events cannot occur at the same time and so it is impossible for A and B to occur together d. Cannot be determined 11. With conditional probability, the sample space is: a. Increased, because we look at the total number of observations b. Decreased, because we reduce our sample space to that of the conditional event only c. Unchanged from that of a simple probability calculation d. Unknown until we perform our calculations 13. If you choose to bet $200 on a round of black jack at the Casino, whilst the person next to you bets $2000, the your risk aversion is an example of: a. Priori classical probability, as you both bet based on prior experiences at the Casino b. Simple probability, because you are simply choosing a random amount of money to assign to the game c. Empirical probability, because you bet based on the known odds of winning d. Subjective probability, because the amount that you bet is based on your personal level of risk SHORT ANSWER QUESTIONS 1. In table 1 below, it shows Ricky Ponting s batting scores for the First Test in each season in his previous 11 years. Table 2 shows the scores that the (mighty) Brisbane Lions achieved in the first 11 games of the 2003 season. Calculate the median and coefficient of variation for each of the data sets using the given information. Table 1 Year Runs scored Table 2 Game Score

4 Answer: Ricky Ponting: Median = 37 Ordered Array is: 5, 11, 20, 26, 31, 37, 76, 88, 96, 141, 149 Mean = Standard Deviation = CV = 83.02% Brisbane Lions: Median = 104 Ordered Array is: 79, 85, 86, 92, 95, 104, 106, 107, 109, 123, 153 Mean = Standard Deviation = CV = 20.11% 2. Define the Coefficient of Correlation and its main features. Use illustrative examples in your answer. A: The Coefficient of Variation is a descriptive statistic that measures the strength and direction of the linear relationship between two quantitative variables. Main features: - unit free - -1 < r < 1 - Close to -1 = strong negative linear relationship - Close to 1 = strong positive linear relationship - Closer to 0 = the weaker any linear relationship - Correlation does not imply causation 3. What are the properties of a binomial distribution? List four as well as a sketch of a right skewed binomial distribution curve. 1. The sample has n observations. 2. Each observation is classified into one of two mutually exclusive and collectively exhaustive categories, usually success of failure. 3. The probability of getting a success if p, while the probability of getting a failure is 1-p. 4. The outcome (i.e. success or failure) of any observation is independent of the outcome of any other observation. 4

5 4. The records of a Cadbury factory show that 20% of chocolates made are inedible and must not be sold to the public. Assuming independence, find the probability of getting: a) 5 inedible chocolates in a batch of b) 8 inedible chocolates in a batch of A study was conducted amongst a group of year old males and females to determine which weekend activities motivate drink driving. It was found that the probability of drink driving amongst this age group is If the person does drink drive, the probability that they have been at a party is The probability of not drink driving and going out to dinner with friends is This probability reduces to 0.03 if they go to dinner and drink drive. Finally, supposing the person does not drink drive, the probability that they have been out clubbing is Assume that the weekend activities are mutually exclusive If a person from the study is chosen at random: Find the probability that the they go to a party and do not drink drive Find the probability of drink driving provided that they go clubbing on the weekend Find the probability of going to a party and drink driving or going out to dinner with friends and drink driving Is drink driving amongst this age group statistically independent of going to a party on the weekend? ANSWER: Step One: specify the events that can occur Drink driving = D Not drink driving = D Going clubbing = C Going to a party = P Going out for dinner with friends = Di Step Two: write down known probabilities in numerical form P(D) = 0.41 P(P D) = 0.73 P(D and Di) = 0.18 P(D and Di) = 0.03 P( C D ) =

6 Step Three: create a joint probability table this will enable you to answer all questions relevant to the example Clubbing (C) Party (P) Dinner (Di) TOTAL Drink Drive (D) Not DD (D ) TOTAL Step Four: answer the questions 1. P(P and D ) = 0.15 (Read straight from the table) 2. P(D C) = P(D and C) = 0.08 = P(C) General Formula: P(A or B) = P(A) + P(B) P(A and B) P( D and P or D and Di ) = P(D and P) + P(D and Di) P( D and P and D and Di ) = = 0.33 NB: the P( D and P and D and Di ) = 0 because we assume that the weekend activities are mutually exclusive they only do the one and therefore they can t go out to dinner and to a party. 4. To prove statistical independence, you must show the following: P(D and P) = P(D)*P(P) P(D)*P(P) = 0.41*0.45 = P(D and P) = 0.30 Therefore, the probability of going to a party and drink driving amongst males and females aged are not statistically independent events. 6. Discuss the different types of probability, giving examples for each and highlighting the relevant benefits of each type. ANSWER: 1) Objective (Classical) a. Priori Classical Probability: based on prior knowledge. For example: we know with certainty that if we flip a coin, P(Head) = 0.5 b. Empirical Classical Probability: based on observed data: For example: betting on horse races based on the horses odds 2) Subjective: involves judgment or personal assessment and will differ from one person to the next. For example: when playing Keno, you choose the numbers that you think will win 6

7 The relative benefit of objective rather than subjective probability is that objective probability is actually based on known/observed probabilities that we have already witnessed. They are therefore better estimates of future outcomes than subjective probabilities as these are totally random outcomes based on each person s individual assessment of the situation. It is therefore very difficult to use subjective probabilities to predict future outcomes because they are variable from one person to the next. 7. If N = 10 and n =5, how many groups should the population be divided into for the purposes of stratified sampling? k =N/n, therefore 10/5 =2 7