Pearson LCCI Certificate in Business Statistics

Pearson LCCI Certificate in Business Statistics Level 3

(ASE20100)

Examiners' Report December 2018

Business Statistics Level 3 December 2018

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December 2018 Publication code: 61394_ER All the material in this publication is copyright ? Pearson Education Ltd 2018

Business Statistics Level 3 December 2018

Introduction

This examination requires a balance between the various stages of a statistical investigation, usually involving the collection of data, basic statistical calculations, the testing of hypotheses and the interpretation of results. To achieve a good grade it is important that a candidate is able to be successful at all of these stages. In general, candidates cope well with the statistical calculations, but struggle with the more discursive aspect of the paper. Overall, the candidate answers seen in this Level 3 paper were of a similar standard to previous papers. Candidates showed a good understanding of many of the numerical techniques required for this examination, but often failed to interpret the numerical answers in a clear way. It is important that candidates become familiar with using data and are able to indicate clearly what the data is showing. It is not sufficient to just perform numerical techniques without interpreting the results of these calculations. In general, candidates gave good answers to those questions that required numerical answers, particularly those questions that required routine calculations (e.g. calculating statistical measures such as the mean of grouped data, the calculation of quality control limits, or the calculation part when carrying out a statistical test or obtaining a confidence interval). However, candidates were generally poor at interpreting and commenting on their answers. Questions involving the use of index numbers, and the topic of sampling methods tend to cause most difficulties for students.

Business Statistics Level 3 December 2018

Question 1

Examiner Comments Parts (a) (i) and (ii) require an understanding of the normal distribution to obtain suitable probabilities. Candidates had little difficulty in computing z scores to obtain probabilities in the early parts, although having got the correct z-scores there were errors in reading or manipulating the probabilities to obtain the correct answers. Part (a) (iii) required the candidates to combine two normal distributions to find the distribution of the sum of two normal distributions. Candidates correctly found the combined mean, but had difficulty in finding the combined standard deviation. Part (b) required candidates to reverse the situation required in part (a) to find a time that 95% of occasions satisfy. Very few candidates were successful at handling this situation. Although a number of candidates worked out that 95% of inspections could be achieved in 22 minutes, very few took this figure away from 4 o'clock to identify that the latest time for an inspection to be started was 15:38 However, most candidate were able to use the normal distribution to calculate the quality control chart limits, and most spotted that the final sample lay outside the action limits. However, very few candidates spotted that the sample means were gradually increasing, indicating that the samples were gradually going out of tolerance. The following is a typical answer.

Business Statistics Level 3 December 2018

Examiner Tip Candidates should become familiar with finding probabilities using the normal distribution. The use of the normal distribution in quality control is a useful application of the distribution.

Business Statistics Level 3 December 2018

Question 2

Examiner Comments In part (a) few candidates were able to describe the concepts of statistical testing and confidence intervals related to a population mean. In parts (a) and (b) many candidates were able to find confidence interval for both a mean and a proportion, but there were poor answers at interpreting the likelihood of a value that falls inside the interval. The following provided a sensible answer.

Part (c) required candidates to find the sample size to obtain a confidence interval of a fixed size. Some candidates struggled with this.

Business Statistics Level 3 December 2018

In part (d) candidates made poor attempts at generating a random sample when given an extract from random normal tables. Most candidates realised that the numbers generated had to lie between 01 and 80, but many repeated values were seen. In (e) and (f) candidates found it difficult to describe how a proportionate stratified sample could be obtained from the given scenario, although some correctly gave an appropriate disadvantage of random sampling. It is advisable that candidates meet concepts involving data collection in a more practical way rather than learning these ideas from basic bookwork. Many candidates made no attempt at this part of the question paper, indicating that candidates were under-prepared with respect to this topic.

Examiner Tip The topics of sampling methods and the various methods of data collection cannot be avoided. It is important that candidates are prepared well for these topics. The best way to get an understanding of data collection is to undertake practical experience. Students do not get a full understanding of this topic by reading books.

Business Statistics Level 3 December 2018

Question 3

Examiner Comments

As usual, the chi squared test in parts (a) and (b) was answered well. In this question, the candidates had to determine the contributions to a chi-square statistic from the table of observed frequencies. The test of association itself caused few difficulties.

However, although candidates had little difficulty in concluding that there was an association between region and whether or not the deliveries tended to be late, very few candidates were able to follow this up by concluding that, overall, the company's delivery record was okay but that the East region needed to improve the timeliness of its deliveries.

Very poor answers were seen in question 3(d) which required the drawing of a histogram when the classes were of different sizes. Very few candidates took the class width into consideration when determining the height of each block. The class frequency is represented by the area of each block, not the height.

Good answers for the mean of grouped data were seen in part (e).

Examiner Tip

The calculations for a chi squared test are well-understood. A clear understanding of the conclusions from such a test, including a comparison between the expected and observed frequencies or sight of the contributions or, to fully understand in what way the two factors may be associated is expected. Candidates are required to do more than carry out the mechanistic calculations of this test.

As with a number of questions, candidates were able to carry out the required calculations. However, some marks are available for commenting on and interpreting the results obtained from these calculations.

The drawing of a statistical diagram is an important way of representing statistical data. Candidates should be able to create a variety of such diagrams. It should be known that the heights of the blocks on a histogram need to take account of the width of each of the classes.

Business Statistics Level 3 December 2018

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