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EXAMINATION FEEDBACK FORM

Module Code: BUSI1074

Session: Autumn 2021 / 22

Module Title: QUANTITATIVE METHODS 1B

Credits: 10

Module Convenor(s): PAOLO DI GIANNATALE, KIAN HOWE ONG

General Comments:

Students are required to be much more rigorous in their answers. Especially, it would be appreciated a larger use of math and statistic notations/formulas as well as more rigorous definitions of the indexes used, especially for price elasticities. In most cases, these lacks are due to either a very shallow/or mnemonic study or just laziness. As a suggestion, students are expected to study more deeply by using books instead of lecture slides only.

Question Specific Comments:

Question 1:

First sub-question of problem 1 asks to derive and maximize a profit function for a firm operating in two different markets (represented by two different groups of consumers). Although the solution was quite simple, some students made two main serious mistakes. First, they maximized profits separately in the two different markets, and this methodological approach has been considered definitely wrong. Consequently, many students also applies the wrong SOCs.

Second, in many cases the profit function was maximized w.r.t. prices instead of quantities. Again, this has been considered as a serious mistake.

The second sub question asks students to calculate elasticities in two different markets, and interpret the results. In this case, the most common mistake was related to the use of a wrong formula for elasticity, but more importantly, most of students didn’t provide a good interpretation of the link between the PED and the final price set by the firm in each market. Finally, the topic of inflection points. No particular problem, here, but some students either forgot the definition of stationarity or just used the first-order derivatives instead of the second-order ones.

Question 2:

Given a production function, here the candidates were supposed to calculate the marginal productivities of labour and capital at a given point. Although this question was quite easy, many of them just provided the general formulas for MPs but they did not compute the corresponding values at that point, and a similar mistake occurred when they were asked to calculated the total differential at sub-question b).

The most difficult point, the sub-question c), is the one where students lost marks, since the calculation of a derivative was found not so easy. No problem, finally, for point d), asking to find the equation of the tangent line to a function at a given point.

Question 3:

Question 3 was asking to calculate a certain number of permutations in a variety of cases. The most common mistake, here, was the use of formula for combinations rather than for permutations, which is considered as a serious mistake. Some students also got completely confused with the concept of ‘probability’, so they tried to solve the problem by using the normal distribution, a totally wrong approach.

Question 4:

This question was an application of Bayes rule to find a conditional probability. The 90% of candidates didn’t have any particular difficulty and they got all marks, but some of them didn’t have any idea of the approach to be used, while some others tried to use a binomial probability distribution, which was having nothing to do with this context. In this case, the mistake was considered as a serious one and more marks were deducted.

Question 5:

Most students answered this question well - the first sub-question cumulates the joint probabilities whilst the second sub-question computes the marginal probabilities from the joint probabilities. Common mistake, here, was confusing the marginal distribution of Y with the marginal distribution of X.

Question 6:

This question calculates discrete probability distribution function (pdf). In sub-question a), one would use a Binomial pdf to calculate the required probability, because the outcomes are discrete involving 55 trials. In sub-question c), one would use Poisson to approximate the probability. Students who miss more points from this question misunderstood the fact that Binomial computes the exact probabilities whilst Poisson should be used just as an approximating distribution. Finally, it was asked to calculate a prob. by using the standard normal distribution, and here many candidates provided incomplete answers due to a missing/wrong use of the prob. tables.

Question 7:

This question is a one-tailed hypothesis test on the left using the normal distribution. Most students answered sub-questions a) and b) well. Some students computed the p-value correctly but do not define or interpret it. Most students defined Type 2 error correctly but did not compute the corresponding probability correctly for various reasons, not computing the threshold according to a left-tailed test or not evaluating the probability under the true value.

Question 8:

This question is a two-tailed hypothesis test using the t-distribution. Most students answer this question very well. A common deduction is where student does not conclude the hypothesis test, and there is evidence to support the claim that there was a change in the average monthly cost of maintaining the cancer patients. Some other students used the wrong critical value associated with 24 degrees of freedom.

Quantitative Information

All students’ exam performance scores:

(This table shows the distribution of scores of students who attempted the Examination)

                                 Overall

Number                       660

90+                             107

80 – 89                        182

70-79                           135

60-69                           86

50-59                           47

40-49                           52

30 - 39                         22

<30                             29

Mean Mark                   71

Standard Deviation       19.65