Past year okt 2010


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Past year okt 2010

  1. 1. CONFIDENTIAL CS/OCT2010/QMT554 UNIVERSITI TEKNOLOGI MARA FINAL EXAMINATION COURSE DATA ANALYSIS COURSE CODE QMT554 EXAMINATION OCTOBER 2010 TIME 3 HOURSINSTRUCTIONS TO CANDIDATES 1. This question paper consists of five (5) questions.2. Answer ALL questions in the Answer Booklet. Start each answer on a new page.3. Do not bring any material into the examination room unless permission is given by the invigilator.4. Please check to make sure that this examination pack consists of: i) the Question Paper ii) a four-page Appendix (Formula List) Hi) an Answer Booklet - provided by the Faculty iv) Statistical tables - provided by the faculty DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO This examination paper consists of 10 printed pages© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  2. 2. CONFIDENTIAL 2 CS/OCT2010/QMT554QUESTION 1a) The tourism industry in Malaysia is an important foreign exchange earner, contributing to economic growth, attracting investments and providing employment. Realizing the importance of tourism industry, the focus of the government is to enhance the countrys position as a leading foreign tourist destination. Amy, a researcher from a well known consulting firm is given a task to determine the level of satisfaction on the services provided at tourist attractions destinations located throughout Malaysia among foreign tourists. Questionnaires are used as the tool for data collection and a random sample of 50 foreign tourists are selected at various tourist visit destinations. Each tourist selected was asked to give a score to the services provided at the tourists visit destinations. In addition, other information such as gender, age, education level, occupation, income, country of origin, reasons for traveling, and length of stay were also recorded. i) State the population for the above study. (1 mark) ii) Does the study involve primary or secondary data? Give a reason to support your answer. (2 marks) iii) Name any three variables from the above study. For each variable chosen, state its type and the most appropriate graphical presentation. (6 marks) iv) Amy is required to summarize and analyze the information collected from the above study. Suggest the appropriate statistical tests that can be used to analyze each of the following hypothesis. a) There are differences in the scores obtained between gender. b) There are differences in the scores obtained among the education level. c) The level of satisfaction is independent of gender. d) There is a relationship between the scores and the income of the foreign tourist. (4 marks)b) The scores (out of 100) given by the foreign tourists to the services provided at the tourist visit destinations are summarized as below: Table 1: Descriptive Statistics Gender N mean median standard minimum maximum skewness deviation Male 28 84 88 7.2 78 92 -1.6667 Female 22 83 80 6.8 75 85 0.9184© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  3. 3. CONFIDENTIAL 3 CS/OCT2010/QMT554 i) How many female foreign tourists are selected in the study? (1 mark) ii) State the lowest score given by the male foreign tourist to the services provided at the tourist visit destinations? (1 mark) iii) State the highest score given to the services provided at the tourist visit destinations? (1 mark) iv) State the skewness of the males scores distribution and explain what it means. (2 marks) v) Which gender is more consistent when giving scores to the services provided at the tourist visit destinations? Give a reason for your answer. (2 marks)QUESTION 2a) The manager of the Royale Star Resort Hotel stated that the mean guest bills during weekends are RM700 or less. A member of the hotels accounting staff noticed that the total charges for guest bills have been increasing in the recent months. A sample of weekend guest bills was taken to test the managers claim. Analysis using SPSS gives the following result. Table 2: One-Sample Statistics N Mean Std. Deviation Std. Error Mean guest bills 20 705.8000 114.56949 25.61852 Table 3: One-Sample Test Test Value = 700 95% Confidence Interval of the Difference t df Sig. (2-tailed) Mean Difference Lower Upper guest bills .226 19 .823 5.80000 -47.8202 59.4202 i) Determine the 95% confidence interval for the mean weekend guest bills. (3 marks) ii) Specify the null and alternative hypothesis for the above test. (2 marks)© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  4. 4. CONFIDENTIAL 4 CS/OCT2010/QMT554 iii) Show that the test statistic t is 0.226. (2 marks) iv) Based on the p-value in the SPSS output, is there sufficient evidence to support the managers claim at 5% significance level? (3 marks)b) The Royale Star Resort Hotel manager also claims that 50% of the guests will be staying at the hotel for their next visit. A survey was carried out and the result was analyzed using SPSS. The output was given in Table 4. Table 4: Binomial Test Asymp. Sig. (2- Category N Observed Prop. Test Prop. tailed) guests Group 1 yes 56 .56 .50 .271 a response Group 2 no 44 .44 Total 100 1.00 a. Based on Z Approximation. i) Specify the null and the alternative hypothesis for the above test. (2 marks) ii) Based on the SPSS output, is there sufficient evidence to support the managers claim at a = 0.05? (3 marks) iii) Determine the 95% confidence interval on the proportion of guest who will be staying at Royale Star Resort Hotel for their next visit. (3 marks) iv) Interpret the confidence interval obtained in iii). (2 marks)QUESTION 3a) The senior chef wants to investigate the difference between the mean price (in RM) between two brands of tomato soup in the market. The chef randomly samples eight stores. Each store sells its own brand (1) and a national brand (2) of tomato soup. The SPSS results for the prices of a can of tomato soup of each brand from different stores was presented in Table 5 and Table 6: Table 5: Group Statistics Brand Type Mean Std. Deviation Std. Error Mean Mean price of tomato soup 1 2.2000 .13352 .04721 2 2.0200 .10690 .03780© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  5. 5. CONFIDENTIAL 5 CS/OCT 2010/QMT554 Table 6: Independent Samples Test Levenes Test for Equality of Variances t-test for Equality of Means 95% Confidence Interval of the Difference Sig. Mean Std. Error F Sig. t df (2-tailed) Difference Difference Lower Upper Mean price of Equal variances .439 .51855 2.97647 14 .01001 .18000 .06047 .05030 .30970 tomato soup assumed Equal variances 2.976 1.33607E1 .01044 .18000 .06047 .04971 .31029 not assumed i) State the hypotheses for the above test. (2 marks) ii) Based on the results, what is the assumption for the variances of the price between two brands of tomato soup? Use a = 0.05. (2 marks) iii) Using the p-value in the SPSS output, do the data provide sufficient evidence to indicate that there is a difference between the mean price of the two brands? Use a = 0.05. (3 marks) iv) State the 95% confidence interval on the mean price for these brands. Does the confidence interval consistent with your answer in iii)? Explain your answer. (4 marks) b) The marketing food consultant was hired to visit a random sample of five food stores across the district of Petaling Jaya to investigate whether the mean net sales had improved. Each store was a part of large franchise of food stores. The consultant taught the managers of each store better ways to advise and display their foods. The net sales for 1 month before and 1 month after the consultants visit were recorded. The data was analyzed by using SPSS and the results as follows: Table 7: Paired Samples Statistics Std. Error Mean N Std. Deviation Mean Pair Sales of food (before visit) 64.3000 5 21.30000 9.52565 1 Sales of food (after visit) 69.2400 5 22.99180 10.28225© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  6. 6. CONFIDENTIAL 6 CS/OCT2010/QMT554 Table 8: Paired Samples Test Paired Differences 95% Confidence Std. Interval of the Sig Std. Error Difference 2-tailed . Mean Deviation Mean Lower Upper t df Pair Sales of food 1 (before visit) - -4.94 3.90103 1.7446 -9.7838 -.0962 -2.83 4 .047 Sales of food (after visit) i) Show how the value of the test statistic for mean is obtained. (3 marks) ii) Using the p-value, is there any sufficient evidence to indicate that the mean net sales have improved? Test at 5% significance level. (6 marks)QUESTION 4a) The program coordinator from Faculty of Hotel and Tourism wanted to investigate the effectiveness of three different teaching methods for Research Methodology course. Students registered for the course were assigned at random into three different classes and will be taught using the three methods. Students marks at the end of semester were recorded in the table below. Table 9: Students marks in three different classes Method I Method II Method III 60 70 80 65 72 82 55 85 80 50 84 90 58 82 92 62 78 98 68 88 95 70 74 90 52 80 95 62 76 90 The SPSS software was used to conduct the analysis of variance using the recoded data. Table 10 gives the output for the analysis done.© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  7. 7. CONFIDENTIAL 7 CS/OCT2010/QMT554 Table 10: ANOVA Sum of Squares df Mean Square F Between Groups 4322.600 2 X Z Within Groups V W Y Total 5404.700 29 Based on the output, answer the following questions: i) How many observations are involved in this study? (1 mark) ii) Compute the values of V, W, X, Y and Z. (4 marks) iii) State the null and alternative hypothesis for this study. (2 marks) iv) Test the hypothesis that the three different teaching methods have an effect on the students performance at a = 0.025. (4 marks)b) A lecturer wanted to know whether the courses offered to the students of Faculty Hotel and Tourism for this semester is suitable to their program based on the students opinions. He distributed a questionnaire to gather information regarding the courses offered and the suitability of the program. The following table shows the results obtained. Ta ble 11: Students opinion towards course offered Do you think the Courses offered course offered suits the Statistics Business Accounting program? Yes 85 60 77 No 20 13 16 Total 105 73 93© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  8. 8. CONFIDENTIAL 8 CS/OCT 2010/QMT554 Below is the two-way contingency table obtained from SPSS output. Table 12: students opinion * course_offered Crosstabulation course_offered Statistics Business Accounting Total opinion yes Count E 60 77 222 Expected Count 86.0 59.8 76.2 222.0 no Count 20 13 16 49 Expected Count 19.0 13.2 F 49.0 Total Count 105 73 93 Expected Count 105.0 73.0 93.0 Table 13: Chi-Square Tests Asymp. Sig. (2- Value df sided) Pearson Chi-Square G 2 .943 Likelihood Ratio .118 2 .943 Linear-by-Linear Association .114 1 .736 N of Valid Cases 271 a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 13.20. i) Compute the value for E, F and G. (4 marks) ii) State the null and alternative hypothesis to test whether there is an association between the courses offered and the students opinion on the suitability of the courses to their program. (2 marks) iii) Based on the p-value, state your decision and conclusion for the above test. Use a=0.05. (3 marks)© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  9. 9. CONFIDENTIAL 9 CS/OCT 2010/QMT554QUESTION 5a) An observation was carried out to determine the relationship between the age of a chef and the time (in minutes) needed to prepare a dish. The table below shows the data recorded by eight randomly selected chefs. Table 14 Age (years) Time (minutes) 23 63 45 52 34 55 50 54 44 50 29 60 36 57 52 50 Below is the output obtained from SPSS. Table 15: Model Summary Adjusted R Std. Error of the Model R R Square Square Estimate 1 .901 a .811 .780 2.193 a. Predictors: (Constant), age Table 16: Coefficients3 Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta t Sig. 1 (Constant) 71.133 3.246 21.914 .000 age -.409 .081 -.901 -5.078 .002 i) Identify the independent and the dependent variables. (2 marks) ii) Prove that the product moment correlation coefficient is -0.901 and explain its meaning. (4 marks) iii) What percentage of the variation in the time taken to prepare a dish is explained by difference in age of chefs? (1 mark) iv) Determine the slope and y-intercept of the regression equation. Interpret the coefficients in the context of the problem. (5 marks)© Hak Cipta Universiti Teknoiogi MARA CONFIDENTIAL
  10. 10. CONFIDENTIAL 10 CS/OCT2010/QMT554 v) Write the complete regression equation. Estimate the time needed for a chef who is 30 years old to prepare a dish. (4 marks)b) A manager wishes to estimate the mean time the housekeeping staff to prepare a guest hotel room. The time is found to be approximately normally distributed with population standard deviation is estimated to be 15 minutes. How many housekeeping staff should be sampled if the researcher wants to be 95% confident of finding that the true mean differs from the sample mean by 5 minutes? (4 marks) END OF QUESTION PAPER© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  11. 11. CONFIDENTIAL APPENDIX 1 CS/OCT2010/QMT554 KEY FORMULAS CONFIDENCE INTERVAL Parameter and description A (1 - a) 100% confidence interval Mean n, for large samples x±z a/2 a or x±z a/2 4n n Mean y, x±t df = n - 1 for small samples a/2 Proportion n P±z J21 r a/2 l V <T, n <J2 (xx-x2)±z a / 2 J — + Difference in means, nx n2 M - M-2, - 1 or for large and s2 s2 independent samples (*,-*2)±za*J—+ — nx n2 1 1 Difference in means, (xl-x2)±ta/2s..— +— df=n 1 + n 2 - 2 M -M • - 1 - 2 nx n2 for small and j(nx-l)s2+(n2-l)s2 independent samples: S P = equal a 2 nx+n2-2 d±tal2 *d df = n - 1 Difference in means Mi " M = M 2 d 2 (2»2 for paired samples 2> 2> - n d = *d = n- DETERMINING THE SAMPLE SIZE Parameter Mean, y. 2 2 n Z a / 22 7 n < " E© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  12. 12. CONFIDENTIAL APPENDIX 2 CS/OCT2010/QMT554 HYPOTHESIS TESTING Null Hypothesis Test statistic „_x~ Mo n r x ~ Mo H 0 : n = x0 aj4n sj4n for large samples Ho: p. = no t=X~^ d f - n1 for small samples Ho! 71 = 7T0 D-7I 7t(1-7l) -X )-(MI-M2) „ _ Oi-*2)-C"i-/"2) Ho: M1 - ^2 = 0 - z = ( * " 2i or z j for large and independent samples y nx n2 nx n2 = U -X7)-(/U,-Uj) — ^ 2 / (x, 2/_^l d f .,_ n < | + n 2_ 2 „ Ho: ju.1 - a2 = 0 f= for small and independent samples: equal a 2 t_d~Md Ho: |Od = 0 sjyfn df = n - 1, where n = no. of pairs© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  13. 13. CONFIDENTIAL APPENDIX 3 CS/OCT2010/QMT554 SIMPLE LINEAR REGRESSION Sum of squares of xy, xx, and yy: » „ = 2 > 2 - ^ a d ss^sy-S^! n Least squares estimates of A and B: 00Jtv b=—- and a=y-bx SSxx Total sum of squares: SST=J]yz —— n Regression sum of squares: SSfi= SS7"-- SSE POD Coefficient of determination: r2 =• SS yy Linear correlation coefficient: r=- jssxxss yy© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
  14. 14. CONFIDENTIAL APPENDIX 4 CS/OCT2010/QMT554 ANALYSIS OF VARIANCE FOR A COMPLETELY RANDOMIZED DESIGN Let: k = the number of different samples (or treatments) nt = the size of sample / T = the sum of the values in sample i n = the number of values in all samples = n ] +« 2 +n 3 +... V x = the sum of the values in all samples = T}+T2+T,+... 2 V x = the sum of the squares of values in all samples Degrees of freedom for the numerator = k-1 Degrees of freedom for the denominator = n-k Total sum of squares: SST = ^x 2 (2» 2 Between-samples sum of squares: r T,2 Tl T} SSB= -J-+-A-+-?-+... CL*)2 n n n 2 i J n Within- samples sum of squares = SST - SSB Variance between samples: MSB= Variance within samples: MSW = ssw {n-k) MSB Test statistic for a one-way ANOVA test: F- MSW© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL