EXAM M&amp;S1 2011 REGULAR + Answers

# EXAM M&amp;S1 2011 REGULAR + Answers - Exam Mathematics...

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Exam “Mathematics and Statistics” part 1 , IBMS 1 st year (Code 18379) 1a) (5 pnt) A Dutch marketing research company executed a marketing research on behalf of a US Telecom firm. The aim of the research project was to provide information that could be used in managerial decision making about the use of telephony by Dutch households. A questionnaire was constructed. The questionnaire (see exhibit 1) contained questions about the use of telephony in Dutch households. Telephone interviews were conducted among 2000 households, using a computerised questionnaire. The study involves approaching the decision-makers concerning telecommunication. You will find the questionnaire in Exhibit I. For each question number in the following table mark the type of variable with an X Question number Type of variable Categorical Numerical Discrete Numerical Continuous Question 3 X Question 5 X Question 8 X Question 12 X Question 14 X 1b) (5 pnt) Examine the questionnaire in Exhibit I. For each question in the following table mark the correct measurement scale with an X Question number Level of measurement Nominal Ordinal Interval Ratio Question 15 X Question 17 X Question 20 X Question 21 X Question 22 X 2) (10 pnt) The following contingency table was constructed, based on the responses on Questions 17 and 23: Overall satisfaction Very Satisfied Somewhat satisfied Dissatisfied or very dissatisfied Total Gender Male 400 120 80 600 Female 1200 130 70 1400 Total 1600 250 150 2000 Construct a contingency table based on column percentages Attention: column percentage adds up to 100% in each column, see page 80. Overall satisfaction Satisfied Neutral Dissatisfied Total Gender Male 25% 48% 53.3% 30% Female 75% 52% 46.7% 70% Total 100% 100% 100% 100% 2

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3) (40 pnt) The following data set describes the cost of the telephone bill (X) and the number of telephones (Y) of a sample of 5 households. X Y 25 2 30 4 35 3 15 1 20 2 For each of the questions below, show your calculation and/or motivation a) (3 pnt) Construct/draw a X-Y scatterplot based on the data above Important: no lines in the graph (see fig. 2.15 page 83) 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 0 10 20 30 40 b) (3 pnt) Calculate the mode of X and Y X: no mode, all frequencies are equal Y: mode = 2 c) (3 pnt) Calculate the median of X and Y Step 1: arrange in ordered array Positioning point = (n + 1)/2 = 3 Median X: 25 Median Y: 2 d) (3 pnt) Calculate the sample mean of X and Y Use formula 3.1 (page 121) Mean X = (15+20+25+30+35)/5 = 125/5 = 25 Mean Y = (1+2+2+3+4)/5 = 12/5 = 2,4 e) (3 pnt) Calculate the range of X Range = highest value - lowest value = 35 – 15 = 20 f) (3 pnt) Calculate the interquartile range of Y Apply rules 1 – 3 (page 148) 4

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Positioning point Q1 = (5+1)/4 = 1.5 ranked value = (1+2)/2 = 1,5 Positioning point Q3 = (3(5+1))/4 = 4,5 ranked value = (3+4)/2 = 3,5 Interquartile range = 3,5 – 1,5 = 2 g) (3 pnt) Calculate z-scores for X and Y X X – mean (X-mean) 2 Y Y - mean (Y – mean) 2 (X – mean) *
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EXAM M&amp;S1 2011 REGULAR + Answers - Exam Mathematics...

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