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LUBS5000M

Quantitative Methods

Mock Exam 2021

Section A - worth 40% of the overall mark

1. A retail organisation has recently been investigating the profitability of its stores in two regions of the country, Region A and Region B, and has obtained the following data:

Using these statistics, what conclusions can you make about the similarities and differences between the profitability of the stores in the two regions?

2. What is a sampling distribution of means and what does the standard error of the mean (STEM) describe?

3. Distinguish between the Binomial and Poisson probability distributions.

(i) On average 2 workers get injured at XTC Ltd every year. What is the probability that 3 or more workers get injured in any two year period?

(ii) A salesperson knows that over the course of her career she

has a 20 per cent chance of making a sale when calling on a customer. One morning she arranges 8 visits. What is the probability that she will make exactly 3 sales?

4. Outline the different sampling methods that can be used to draw a representative sample of observations from its population and give examples of when each method is appropriate.

Section B – worth 60% of the overall mark

Answer all questions

1(a) Outline the s tandard procedure for carrying out a hypothesis test

(b) Explain how the form of the hypothesis test carried out on means and proportions depends on:

(i) the size of the sample

(ii) the number of samples

(c ) What form of hypothesis tests can be carried out on ordered rather than measured data?

(d) The label on a pack of light bulbs states that it contains ‘life-long’ bulbs with an average life of 975 hours. However, an unhappy customer files a complaint with the Department of Trading Standards alleging that this claim is false and that the life is considerably less than 975 hours. Tests carried out independently on behalf of the Department of Trading Standards found that in a random sample of 25 light bulbs the average life of the bulbs was 956 hours with a standard deviation of 58 hours. Do the results of this test support the company’s claim at a 5% level of significance or does the Department need to take action against the company?

(e) The marketing department of ABC Ltd is interested in assessing whether those people who currently buy cars from a rival do so because they view ABC’s cars as being of poor quality. In carrying out a survey, the marketing department asked 200 people two questions. Firstly, have you purchased a car from ABC in the last month? Secondly, which of the following best describes your view of the quality of cars sold by ABC? The responses to these questions are shown in the Table below.

Is there evidence of an association between customers’ purchasing behaviour and their perception of the quality of cars sold by ABC Ltd? Explain your results in terms that would be comprehensible to a manager with little knowledge of statistics.

2. .The following ordinary least squares regression model reports the findings of research into the relationship between an individuals wage and their personal characteristics such as age, education, experience and gender.

(a) The standard error of provides a measure of the accuracy with which the coefficients are estimated. Discuss the three factors that affect whether is an accurate estimate of the true β