UNIVERSITY of LIMERICK OLLSCOIL LUIMNIGH COLLEGE OF INFORMATICS AND ELECTRONICS. MODULE CODE: MA4125 SEMESTER: Autumn 2003/2004

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1 UNIVERSITY of LIMERICK OLLSCOIL LUIMNIGH COLLEGE OF INFORMATICS AND ELECTRONICS END OF SEMESTER ASSESSMENT PAPER MODULE CODE: MA4125 SEMESTER: Autumn 2003/2004 MODULE TITLE: Computer Aided DURATION: 2½ hours Data Analysis LECTURER: EXTERNAL EXAMINER: Dr. Ailish Hannigan Prof. P.J. Boland INSTRUCTIONS TO CANDIDATES: Answer any 4 questions (each question is worth 20 marks). Calculators may be used. This exam is worth 60% of your final grade.

2 Q1. (a) What is the aim of research? What makes research in business different from other types of research? (4 marks) (b) Distinguish between empirical research and theoretical research. What are the phases of the research process? (6 marks) (c) A researcher wanted to find out how long, on average, Internet users in Ireland spent on-line per week. Visitors to the website of an Irish on-line service provider were asked to fill in a brief questionnaire stating how long they spent on-line per week. 100 visitors to the website filled in the questionnaire and on average, they spent 10 hours per week on-line. (i) Identify the population, the sampling method and the sample in this study. (ii) What is the variable of interest in this study? (iii) What is the main parameter of interest in this study? (iv) What is the best estimate of this parameter? (v) Describe the potential bias in this study. (10 marks) Q2. A survey of a bank s credit card customers was carried out to establish the levels of personal debt of the customers. Data on the following variables were collected from a sample of 60 customers: Amount: ( s) amount currently owed on your credit card Age group: 1 = under 35 and 2 = 35 or older Gender: 1=male, 2=female Otherln: Other personal loans for example car and holiday loans where 1=none, 2=loans less than or equal to 10,000 and 3=loans greater than 10,000 Using the following output from SPSS: (a) Write a newspaper report (suitable for a general audience). (b) Write a detailed statistical report. (8 marks) (12 marks) (Question 2 contd.) 2

3 Valid under 35 >= 35 Total AGEGROUP Cumulative Frequency Percent Valid Percent Percent Valid male female Total GENDER Cumulative Frequency Percent Valid Percent Percent OTHERLN Valid no personal loans loans <= 10,000 loans > 10,000 Total Cumulative Frequency Percent Valid Percent Percent Descriptives AMOUNT Mean 95% Confidence Interval for Mean Lower Bound Upper Bound Statistic Std. Error % Trimmed Mean Median Variance Std. Deviation Minimum Maximum Range Interquartile Range Skewness Kurtosis (Question 2 contd.) 3

4 Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig. AMOUNT * *. This is a lower bound of the true significance. a. Lilliefors Significance Correction 3 Normal Q-Q Plot of AMOUNT Expected Normal Observed Value N = 60 AMOUNT (Question 2 contd.) 4

5 Descriptives AMOUNT AGEGROUP under 35 Mean 95% Confidence Interval for Mean Lower Bound Upper Bound Statistic Std. Error >= 35 5% Trimmed Mean Median Variance Std. Deviation Minimum Maximum Range Interquartile Range Skewness Kurtosis Mean 95% Confidence Interval for Mean Lower Bound Upper Bound % Trimmed Mean Median Variance Std. Deviation Minimum Maximum Range Interquartile Range Skewness Kurtosis AMOUNT AGEGROUP under 35 >= 35 Tests of Normality Kolmogorov-Smirnov a Statistic df Sig. Statistic df Sig * *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Shapiro-Wilk (Question 2 contd.) 5

6 AMOUNT 300 N = under 35 >= 35 AGEGROUP AGEGROUP * OTHERLN Crosstabulation AGEGROUP Total under 35 >= 35 Count % within AGEGROUP % within OTHERLN % of Total Count % within AGEGROUP % within OTHERLN % of Total Count % within AGEGROUP % within OTHERLN % of Total OTHERLN no personal loans < loans > loans 10,000 10,000 Total % 43.3% 33.3% 100.0% 35.0% 50.0% 71.4% 50.0% 11.7% 21.7% 16.7% 50.0% % 43.3% 13.3% 100.0% 65.0% 50.0% 28.6% 50.0% 21.7% 21.7% 6.7% 50.0% % 43.3% 23.3% 100.0% 100.0% 100.0% 100.0% 100.0% 33.3% 43.3% 23.3% 100.0% 6

7 Q3. (a) Four questions from a questionnaire used in a graduate employment survey are as follows: Q1. Are you Male Female? Q2. How much do you earn per year? Under 15,000 15,000 30,000 30,000 45,000 45,000 60,000 60,000 + Q3. Rate the relevance of your degree to your chosen career on a scale of 0 to 10 where 0 is no relevance. Q4. How many years post-graduate experience have you? Classify the data generated for each of the above questions by data type and scale of measurement. (6 marks) (b) Statistical errors can occur in the planning, design, execution and analysis of a study and in the presentation and interpretation of the results. Discuss with reference to at least eight common statistical errors. (8 marks) (c) Correlation and regression are among the most commonly used statistical tools. Write a note on cautions about the use and interpretation of these tools. (6 marks) Q4. (a) Define a p-value. (2 marks) (b) A hypothesis test was carried out to investigate if there was a difference between the mean hourly wage ( s) of non-irish nationals and Irish nationals working in the service industry. Write a statistical report on the results of the analysis using the output from SPSS below. (10 marks) (Question 4 contd.) 7

8 PAY NATION Irish non-irish Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig * * *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Group Statistics PAY NATION Irish non-irish Std. Error N Mean Std. Deviation Mean E-02 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2- tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference PAY Equal variances assumed Equal variances not assumed Lower Upper (b) An estate agent claims that the average monthly rent for a two-bedroom apartment in Limerick is 600. A random sample of 40 advertisements for two-bedroom apartments in the local newspaper was selected. The monthly rents advertised were summarised using SPSS and a hypothesis test was carried out to investigate the estate agent s claim. Assume the data are normally distributed. Write a statistical report on the results of the analysis using the output below. (8 marks) (Question 4 contd.) 8

9 One-Sample Statistics RENT Std. Error N Mean Std. Deviation Mean One-Sample Test RENT Test Value = % Confidence Interval of the Mean Difference t df Sig. (2-tailed) Difference Lower Upper Q5. (a) Sales of major appliances such as washing machines and dishwashers are thought to vary with the new housing market. A trade association collected data (in thousands of units) on major appliance sales and housing starts. The data were analysed using simple linear regression and the output from MINITAB is given below. Write a statistical report on the output. (10 marks) The regression equation is appliance sales = housing starts Predictor Coef SE Coef T P Constant housing S = R-Sq = 83.2% R-Sq(adj) = 81.1% Analysis of Variance Source DF SS MS F P Regression Residual Error Total Unusual Observations Obs housing applianc Fit SE Fit Residual St Resid R R denotes an observation with a large standardized residual (Question 5 contd.) 9

10 3 Histogram of the Residuals (response is appliance) Histogram of the Residuals (response is appliance) 3 Frequency Frequency Standardized Residual Standardized Residual Normal Probability Plot of the Residuals (response is applianc) 1 Normal Score Standardized Residual (Question 5 contd.) 10

11 Residuals Versus the Fitted Values (response is applianc) Standardized Residual Fitted Value (b) A survey of customers of a fast-food restaurant was carried out where each customer was asked which one of the following aspects of the restaurant they rated as most important: cleanliness, speed of service, quality of the food or value for money. The gender of the customer was also recorded. The data collected were analysed using SPSS and a chisquare test was carried out to investigate if there was an association between the gender of the customer and the aspect of the restaurant they rated as most important. Use the output on the next page to answer the following questions: (i) What percentage of female customers rate cleanliness as the most important aspect of the restaurant? What percentage of customers who rate speed as the most important aspect of the restaurant are males? What percentage of the total number of customers surveyed rate value for money as the most important aspect of the restaurant? (ii) (iii) (iv) (v) What is the null hypothesis for the chi-square test in this example? What is your conclusion from the results of the hypothesis test? Does the rule of thumb for the chi-square test hold for this example? What is the nature of the relationship between gender and the aspect of the restaurant rated as the most important? (10 marks) (Question 5 contd.) 11

12 GENDER * ASPECT Crosstabulation GENDER Total Female Male Count Expected Count % within GENDER % within ASPECT % of Total Count Expected Count % within GENDER % within ASPECT % of Total Count Expected Count % within GENDER % within ASPECT % of Total ASPECT Cleanliness Speed Quality Value Total % 16.1% 11.3% 30.6% 100.0% 76.5% 37.0% 33.3% 45.2% 50.0% 21.0% 8.1% 5.6% 15.3% 50.0% % 27.4% 22.6% 37.1% 100.0% 23.5% 63.0% 66.7% 54.8% 50.0% 6.5% 13.7% 11.3% 18.5% 50.0% % 21.8% 16.9% 33.9% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 27.4% 21.8% 16.9% 33.9% 100.0% Chi-Square Tests Pearson Chi-Square Likelihood Ratio Linear-by-Linear Association N of Valid Cases Asymp. Sig. Value df (2-sided) a a. 0 cells (.0%) have expected count less than 5. The minimum expected count is