UNIVERSITI UTARA MALAYSIA COLLEGE OF ARTS AND SCIENCES SCHOOL OF QUANTITATIVE SCIENCES GROUP ASSIGNMENT SQQS1013 ELEMENTARY STATISTICS 2nd SEMESTER SESSION 2012/2013 INSTRUCTIONS: 1 - Assignment Statistics introduction. Five (5) persons in a group. 2. Answer ALL questions and show all your calculations clearly. 3. Report must be typewritten using A4 paper. 4. Every question and answers must be written on a new page. 5. The front cover for the report is as in Appendix 1. 6. Total marks: 90. 7. Evaluation of the report will be as follows: Front cover, table of contents, references, font, etc – 10 marks • Answers to all 4 questions – 80 marks. 8. Due date: 9 May 2013 _________________________________________________________________________________ QUESTION 1 (15 MARKS) As a member of the marketing team at an Internet music site, you want to understand your customer preferences when visiting your website. You are interested to know their choice of search engine and how many hours they spend in a week browsing the website. A survey was conducted on 30 visitors to the site and the information collected is recorded in TABLE 1 below.
TABLE 1 | |Gender |Age |Search Engine |Time spend per week (in | | | | | |hours) | |1 |Male |16 |Google |25. 4 | |2 |Male |21 |Google |20. 4 | |3 |Female |14 |Direct |21. | |4 |Male |30 |Yahoo |15. 7 | |5 |Female |28 |Google |27. 6 | |6 |Female |15 |Direct |22. 5 | |7 |Female |18 |Google |20. 9 | |8 |Male |14 |SnapLink |18. | |9 |Female |22 |Google |34. 5 | |10 |Male |14 |MSN |29. 8 | |11 |Male |15 |Google |8. 5 | |12 |Female |29 |Yahoo |11. 9 | |13 |Female |35 |Google |29. | |14 |Male |17 |Yahoo |26. 5 | |15 |Female |20 |Yahoo |31. 8 | |16 |Male |17 |MSN |19. 0 | |17 |Male |28 |Direct |18. 0 | |18 |Female |26 |Google |15. | |19 |Male |19 |Direct |10. 8 | |20 |Female |18 |SnapLink |9. 2 | |21 |Female |21 |MSN |41. 0 | |22 |Male |20 |Yahoo |10. 8 | |23 |Female |19 |Google |17. | |24 |Female |20 |Yahoo |9. 6 | |25 |Female |17 |MSN |30. 7 | |26 |Male |26 |Direct |24. 3 | |27 |Female |25 |Others |20. 9 | |28 |Male |25 |Yahoo |24. | |29 |Female |24 |Direct |26. 5 | |30 |Male |15 |Google |38. 0 | a) State ALL the variables and the measurement scale involved in the survey. (4) b) Construct a suitable chart to summarize each of the qualitative variables in the survey. (6) c) Construct a stem and leaf diagram for the time spend per week browsing the website.
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What can you conclude about the distribution of the time spend per week browsing the site? (5) QUESTION 2 (25 MARKS) Referring to the information given in TABLE 1, a) Use the Sturge’s Rule to construct a frequency distribution for the time spends per week browsing the site. (4) b) Using the frequency distribution in (a), calculate the mean time spend per week browsing the site. (3) c) Using the raw data in TABLE 1, calculate the mean time spend per week browsing the site. (2) d) Briefly comment on the values obtained in (b) and (c). 2) e) Estimate the mode of time spend per week browsing the site by drawing a histogram (4) f) Estimate the median of time spend per week browsing the site by drawing an ogive ‘less than’ (4) g) Calculate the standard deviation of time spend per week browsing the site. (3) h) Discuss the shape of the distribution of the time spend per week browsing the site by showing relevant calculations. (3) QUESTION 3 (20 MARKS) Samples arriving at a certain laboratory may be given a number of tests to determine the presence of Chemical X. If the result of test A is positive, then the sample is subjected to test B.
If the result of test B is positive, then it is subjected to test C. If the result of test C is positive, then it is assumed that the sample contains Chemical X. Suppose that the probabilities of false positive for test A, B, and C are 0. 05, 0. 10 and 0. 15 respectively, and the probabilities of false negatives are 0. 01, 0. 02 and 0. 03 respectively. Furthermore, suppose that 10% of samples arriving at the laboratory contain Chemical X. a) Using the given notations, draw a complete tree diagram for the above testing process. (8) ( X+ and X- denote, respectively, the presence and absence of Chemical X in the sample.
A+, A-, B+, B-, C+ and C- denote, respectively, the result of positive and the result of negative in the respective tests. ) b) Find the probability that the laboratory will falsely assume the presence of Chemical X in a sample. Give your comment about the possible mistake made by the laboratory about the presence of Chemical X based on the probability value obtained. (5) c) What is the percentage of samples tested by the laboratory are reported to contain Chemical X? Give a brief interpretation of the value obtained. (7) QUESTION 4 (20 MARKS)
A farmer will earn a profit of RM28,000 in case of heavy rain next year, RM55,000 in case of moderate rain, RM15,000 in case of little rain, and RM7,000 in case of no rain. A meteorologist forecasts that the probability is 0. 30 for heavy rain, 0. 35 for moderate rain, 0. 20 for little rain, and 0. 15 for no rain next year. a) Write the probability distribution of next year’s profit for this farmer. (3) b) Construct the cumulative probability distribution of next year’s profit for this farmer. (3) c) Calculate the expected of next year’s profit in thousands of ringgits for this farmer.
Give a brief interpretation of the value obtained. (5) d) Calculate the standard deviation of next year’s profit in thousands of ringgits for this farmer. (4) e) Discuss the meaning of standard deviation of the random variable focusing on the values obtained in (c) and (d) above. (5) APPENDIX 1 ———————– [pic] UNIVERSITI UTARA MALAYSIA COLLEGE OF ARTS AND SCIENCES SCHOOL OF QUANTITATIVE SCIENCES 2nd SEMESTER SESSION 2012/2013 SQQS1013 ELEMENTARY STATISTICS GROUP ASSIGNMENT YOUR LECTURER’S NAME GROUP NO: (example A12) | |MATRIC.
NO |NAME | |1 | | | |2 | | | |3 | | | |4 | | | |5 | | | SUBMITTED DATE 9 May 2013