UNIVERSITY OF TECHNOLOGY, JAMAICA FACULTY: SCIENCE AND SPORT SCHOOL: MATHEMATICS AND STATISTICS Final Examination: Semester 1, Academic Year 2016/17 Module Name: Business Statistics Module Code: STA2004 Date: December, 2016 Theory/Practical: Theory Groups: BBA2/ EBBA2/ PBBA2/BSc. Accounting/BSc. Economics/ BSc. Entrepreneurship Duration: 2 Hours Instructions 1. This paper has four (4) pages and six (6) questions. 2. Answer ANY FOUR (4) questions. 3. Begin the answer to each question on a new page. 4. Statistical Booklets are provided. 5. No pen, pencil, or any other mark should be made on the list of formulae and set of statistical tables. 6. Candidates are allowed to use silent electronic calculators. DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO 2 QUESTION # 1 (a) The following table gives the frequency distribution of the duration (in minutes) of 100 long-distance calls made by persons using TVI longdistance service. Duration (minutes) 0 - 4 5 - 9 10 - 14 15 - 19 20 - 24 Frequency 8 22 35 20 15 Calculate: (i) the mean (ii) the median (iii) the standard deviation. [3+3+4 marks] (b) A group of 150 randomly selected chief executive officers (CEOs) were tested for personality type. The following table gives the result of this survey. Type A Type B Male 78 42 Female 19 11 If one CEO is selected at random from this group, find the probability that this CEO (i) has a type A personality and is female (ii) has a type B personality given that the person is a female [2+3 marks] QUESTION # 2 (a) Five percent of all DVDs manufactured by a large electronics firm are defective. A quality control inspector randomly selects 10 DVDs from the production line. (i) Find the probability that exactly 3 of these DVDs are defective. (ii) Find the probability that at least 2 of these DVDs are defective. (iii) Calculate the standard deviation of this probability distribution? [2+3+2 marks] (b) Customers arrive randomly at a supermarket in Kingston at an average rate of 8 per minute. Assuming the customer arrivals forms a Poisson distribution, calculate the probability that: (i) two customers arrive in a minute (ii) at least one customer arrive in any 45 second period (iii) at most 2 customers arrive in any 30 second period. [2+3+3 marks] 3 QUESTION # 3 (a) A food company is planning to market a new ice cream. However, before marketing this ice cream, the company wants to find what percentage of people will like it. The company's research department selected a random sample of 400 persons and asked them to taste this ice cream. Of these 400 persons, 224 said they liked it. (i) What is the point estimate of the proportion of all persons who like this ice cream? (ii) Calculate a 95% confidence interval estimate of the proportion of all persons who like this ice cream. (iii) Interpret the interval constructed in part (ii). [1+3+2 marks] (b) A company that produces detergents wants to estimate the mean amount of detergent in 64-ounce boxes at a 99% confidence level. The company knows that the standard deviation of amounts of detergent in such boxes is 0.2 ounces. How large a sample should the company take so that the estimate is within 0.04 ounces of the population mean? [3 marks] (c) The management at the New Century Bank claims that the mean waiting time for all customers at its branches is less than that at the Public Bank, which is its main competitor. A business consulting firm took a sample of 200 customers from the New Century Bank and found that they waited an average of 4.60 minutes with a standard deviation of 1.2 minutes before being served. Another sample of 300 customers taken from the Public Bank showed that these customers waited an average of 4.85 minutes with a standard deviation of 1.5 minutes before being served. Test at the 5% significance level if the claim of the management of the New Century Bank is true. [6 marks] QUESTION # 4 (a) The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 25 such batteries and found that the mean life of this sample is 43.75 months with a standard deviation of 4 months. Using the 5% significance level, would you conclude that the mean life of these batteries is less than 45 months? [5 marks] (b) The marketing director for a metropolitan daily newspaper is studying the relationship between the type of community the reader lives in and the portion of the paper he or she reads first. For a sample of readers the following information was collected. National News Sports Comics Total Urban 170 124 90 384 Rural 120 112 100 332 Farm 130 90 88 308 Total 420 326 278 1024 At the 0.01 significance level, can we conclude there is a relationship between the type of community where person resides and the portion of the paper read first? [10 marks] 4 QUESTION # 5 (a) The registrar at University of Jamaica studied the grade point averages (GPAs) of students over many years. She discovered that the distribution is approximately normal with a mean of 2.80 and a standard deviation of 0.40. (i) What percent of the students are on probation, that is, have a GPA less than 2.00? (ii) The student population at University of Jamaica is 10,000. How many students are on the dean's list, that is, have GPAs of 3.70 or higher? (iii) To qualify for a Bell scholarship, a student must be in the top 5 percent of the student body. What GPA must a student have to qualify for a Bell scholarship? [3+4+4 marks] (b) At Jen and Perry Ice Cream Company, the machine that fills one-pound cartons of Top Flavour ice cream is set to dispense 16 ounces of ice cream in every carton. However, some cartons contain slightly less than and some contain slightly more than 16 ounces of ice cream. The amounts of ice cream in all such cartons have a normal distribution with a mean of 16 ounces and a standard deviation of 0.18 ounces. Find the probability that the mean amount of ice cream in a random sample of 25 such cartons will be less than 15.95 ounces. [4 marks] QUESTION # 6 The following data give information on the ages (in years) and the number of breakdowns during the past month for a sample of seven machines at a large company. Age (X) 12 7 2 8 13 9 4 Number of breakdowns(Y) 9 5 1 4 11 7 2 (a) Find the equation of the least squares regression line. (b) Predict the number of breakdowns when the age of a machine is 10. (c) Compute the product moment correlation coefficient and interpret your answer. (d) Compute the coefficient of determination and interpret your answer. [7+2+4+2 marks] **** END OF PAPER ***